Sorry to hear of your very bad day, which must have been so hard for you both. You have from what you say been trying your best to do the best for your Mum. This in itself is no easy task as all of us on TP know. Both physically and mentally draining and such a constant worry.
You have for whatever reason come to the conclusion that she will be safer where she is and unsurprisingly, it has been a wake up call for her as you say. But you must feel guilty in any way because she will miss her garden etc. think of how you would feel if she wandered into the garden and fell, and was left out there for a period of time?
You can also tell her about the garden, or remenise about it with her which she will relate to. You can fabricate if you think it will make her feel better. It's early days in her new residence and it may take her a few weeks to settle from what others have said. In that time you will be worried about her obviously, but at least you know she will be looked after by more than one person day and night, who are on call if needed. She will be fed so no more concerns about if she's eating or can she cook or did she remember to.
It will get easier I'm sure and she knows really that it is for the best but feels probably like we did on our first day at school, overwhelmed not understanding fully, and making the best of it.
Don't feel guilty for a second more, it's not you that has put her in the home it's the disease called dementia. You never did this to her physically or mentally did you the dementia did unfortunately. Cry, because you need to. Cry, because you feel another step nearer to losing your Mum. Cry because for every pound you had you would no doubt love to make her how she used to be. But please don't cry because you feel guilty about doing the best you could for her just like you always have and will.
One day at a time.