Did I make the right choice for mom?

There is no "right choice" in these times. There is only the best choice we can make taking into account the safety of the elder. She already had this serious incident. There would be others, esp because she refused rehab and didn't work to get back on her feet. Let's say best world she DID get back on her feet, you know she is now at the stage or soon will be where truly every second at home alone she is in danger. How much better could you sleep knowing that.
I am with the idea of letting her acclimate. There is no "good" here. There may never again be a really "happy" here. But the truth is everyone is doing the best that they are able for her. Not everything has an answer. You are trying to do as you think is best. That is the best you can do. When the circular thinking comes at you just push it away and tell yourself you already thought about that today, and there is no answer, and you will run it by again tomorrow. It just cannot be that our every thought is taken up with all this. It is so dreadful to have to witness this anquish in those we love. So sorry for all you are both going through.

musame, please note that when a person has dementia and they say they want "to go home", the house they are referring is their childhood home.

My Mom [98] kept telling me she wanted to go home, and at first I thought it was the house that she and Dad had shared. It wasn't until a month later I realized she wanted to go back to the house where she grew up to see her parents and her siblings. Then I found out that is the norm.

You made the right decision about Assisted Living/Memory Care. The Staff knows exactly what to do in various situations. Seven days isn't enough time for your Mom to start to feel "at home" in her new surroundings. And yes, it is best not to see Mom for 3 to 4 weeks so she can adjust. Even after that time frame, best not to visit daily for hours on end, otherwise your Mom won't want to join any of the activities, if so inclined.

Musame,
Your mother sounds like what we are going through with my mom, she was recently moved to independent living after 40 years of living in the same apartment community. Mom has been diagnosed with dementia all classic signs memory loss, highly agitation, hallucinations, paranoia, decline in hygiene and more.

The transition to care facility has been traumatic for her, and she constantly talks about going back home in her case she’s very clear she means former home she moved from. She also says facility and staff are nice but it’s not her home. When we tell her previous home no longer is hers, she doesn’t understand how that could be.

I have been told by caregiver and mom’s social worker to step back my contact with her to give her time to acclimate to new surroundings. I now speak with head caregiver several times weekly and mom seems to be doing well except for sleep issues, seeing me has been a trigger for her. This has been a hard process but I have no doubt that this was best decision for mom’s well being.

You did the right thing, let her settle in. Sounds like you are doing some grieving already and she is still here. Give her and her facility a chance.

Your mom is brand new to Memory Care, so this 'going home' info may not apply to her at this precise moment. It may apply to her down the road, however, and prove useful to you at some point:

Why someone with dementia asks to go home
Alzheimer’s and dementia damage the brain and cause a person to experience the world in different ways. 
So, what we hear as “I want to go home” is often a request for comfort rather than literally asking to go somewhere.
The kindest thing to do is to meet them where they are, focus on comfort and reassurance, and respond to the emotions behind their request. The goal is to reduce your older adult’s anxiety or fear so they can let go of the idea.
Helping them to calm down also gives you a chance to check if discomfort, pain, or a physical need is causing this behavior.

3 kind, calming ways to respond to “I want to go home”
These suggestions will put you on the right track, but it’s a good idea to get creative and come up with responses that are tailored for your older adult’s history, personality, and preferences.
1. Reassure and comfort​ to validate their needs
Sometimes saying “I want to go home” is how your older adult tells you they’re tense, anxious, scared, or in need of extra comfort. 
By responding in a calm and positive manner, you’ll validate their needs and feelings. This helps them feel understood and supported.
Approach your older adult with a calm, soothing, and relaxed manner. If you remain calm, it often helps them calm down too.
If they like hugs, this is a good time for one. Others may prefer gentle touching or stroking on their arm or shoulder or simply having you sit with them.
Another way of giving extra comfort and reassurance is to give them a soothing blanket, therapy doll, or stuffed animal.

2. Avoid reasoning and explanations
Trying to use reason and logic isn’t recommended when someone has a brain disease. It will only make them more insistent, agitated, and upset.
Don’t try to explain that they’re in their own home, assisted living is now their home, or they moved in with you 3 years ago.
They won’t be able to process that information and will feel like you’re not listening, you don’t care, or that you’re stopping them from doing something that’s important to them.

3. Validate, redirect, and distract
Being able to redirect and distract is an effective dementia care technique. It’s a skill that improves with practice, so don’t feel discouraged if the first few attempts don’t work perfectly.
First, agree and validate
Agree by saying something like “Ok, we’ll go soon.” or “That’s a good idea. We’ll go as soon as I clean up these dishes.” This calms the situation because you’re not telling them they’re wrong.
Next, redirect and distract
After agreeing, subtly redirect their attention. This redirection should lead into pleasant and distracting activities that take their minds away from wanting to go home.
For example, you could gently take their elbow while saying “Ok, we’ll go soon” and walk down the hall together to a big window or to the kitchen. Point out some of the beautiful birds and flowers outside or offer a snack or drink they like. Later, casually shift to another activity that’s part of their daily routine.
Another example is saying “Ok, let’s get your sweater so you won’t be cold when we go outside.” Then, while you’re both walking to get the sweater and chatting about something pleasant, stop for a cup of tea or get involved in an activity they enjoy.
Or, ask them to tell you about their home. After a while, guide the conversation to a neutral topic.
Asking about their home validates their feelings, encourages them to share positive memories, and distracts them from their original goal of going home. Open questions that encourage them to share their thoughts work well.
For example:
Your home sounds lovely, tell me more about it.
What’s the first thing you’re going to do when you get home?
What is your favorite room of the house?
Continued :

What to do if they refuse to let go of the idea
Sometimes, your older adult will refuse to let go of the idea of going home, no matter how much you try to soothe

If that happens, you might need to agree to take them home and then go for a brief car ride.
Experiment with how long it takes before you can take them home without protest. Or, suggest a stop at the ice cream shop, drugstore, or grocery store to distract and redirect.
If it’s not possible to actually take them out or get into the car, even going through the actions of getting ready to leave can still be soothing. This will shows that you agree with them and are helping to achieve their goal.
Meanwhile, the activities of getting ready give you more chances to distract and redirect to something else.
Keep in mind that not everything you try will work the first time. And even if something works once, it might not work the next time. Do your best to stay calm, flexible, and creative – this technique gets easier with practice.

Also, it's always a good idea to play music when an elder gets agitated. It normally has a very calming effect on them.

With women, sometimes giving them a baby doll to hold & coddle helps A LOT. It's something they can remember, something they can relate to, and something to do that feels constructive and motherly.

Best of luck! I hope some of these techniques work!

My Mama has been in Memory care for 1 year. She is about in year 11 of Alzheimer's so say the neurologists. She still wants to go home. But F.F. is right. Sometime in here it has changed and means the house she grew up in. With her Daddy, Mama sister and brothers. She still will ask when can I go home? She does fine there and does activities now and has friends. But She will not change. But I did. You learn to tell fiblets, Little white lies. You ask questions about home. You change the subject. You take her on a walk. Get out that photo album. My Mama does not even need a walker yet so this is going to be a long haul. Pace yourself. We are all going to live thru this. It does get better. The big job is done. You made it to Memory care. That is a feat in itself for most all of us! Hang in there you are not alone.