She will become situated over time and adjust to the idea of being there. If possible, when you visit her, try not to cry because it may upset her more.
You know from a logical perspective that caring for her in your home was taking a toll on you. From emotional perspective, you are feeling guilt and worry about her wellbeing.
The next time you visit or speak to her, try to point out to her what may be a positive side of being there- meeting new people, engaging in different activities, having helpers around her, etc.
You are crying because you miss her, because of the nature of her condition, as a result of having become burned out and because you worry about her being away from home. This is a stage that you're experiencing grieving for having to place her in the care home. It is something that over time will subside as you become more confident in knowing that you've done what is best for her at this time. It may not seem as the best option to you because you're comparing how she was at home and how she's at the care home. These are two different scenarios though and comparison may not do justice to her new placement.
It may be helpful to get connected to other care givers who take care of those with dementia. If such groups exist in your area, you can get a lot of emotional support and strength through these meetings. If these are not available or your schedule prevents you from joining, there are some free online support groups available.
In order to move forward, you would want to remind yourself that this is the best option for her at this moment in time. It takes people time to adjust to novel situations and as you focus on some of the positive things that she is receiving there and able to experience, speak to her about these when you talk to her.
Your guilt and fear stem from doubting how others will care for her and because you feel that you should be able to do more for her. But, caring for someone with this condition is very difficult and in most cases caregivers resort to professional support (care homes). A part of dealing with your guilt and crying spells is to accept your limitations as a human being and to forgive yourself for pushing yourself too hard.
Online Support Groups for Caregivers of People With Dementia ...