My mother is in a nursing home, but remains totally dependent on me for her companionship and emotional sustenance. I have been trying to visit daily, but I need respite at times. I skipped a day, and found her to be quite despondent the next day. She will rarely leave her room, and hasn't connected to any of the other residents, nor will she open up to staff. The residents in her home like unit are not as aware as my mother, though there are others that are in nearby "houses". She turns down everything the activities director suggests. Our family is very small, so there aren't many visitors.
Dad has been in one place or another since February of this year. Initially he seemed quite dependent on my visits and always asked before I left when I was coming back. At first, I tried to go every day but it was exhausting and so I dropped down to every other day.. Yes, I felt guilty when I stopped going every single day. Just like you state, I was Dad's only regular visitor and he had few other visitors.
The good news for Dad is that he is finally becoming acclimated to his new "home". Although he doesn't participate in activities (yet) --- he has found and made a couple of friends. Just like your Mom, my Dad seems more aware than a lot of the residents there so I wasn't sure how he was going to get along with everyone else.
The other thing is that in Dad's case whenever I visited him, he'd just be sitting there in his wheelchair in his room. Just the other day, we had a care plan meeting and I was concerned that he didn't know the staff well enough to ask for assistance when he needed it. I found out that he interacts with staff far more than I realized.
My point is that we're looking at it from our perspective and with a great deal of empathy because we are caregivers after all. However, just like dropping our child off for the first day of school, he or she may be out of sorts at the beginning but it's a process ... children do adjust to new environments that are ultimately the best for their well-being. I've come to believe these past few months that the elderly are resilient too.
Our parents are going to be ok --- the whole point of Dad going to a facility was to make sure he was safe and well taken care of because caring for him at home was getting to be too much.
I am now struggling with the idea of cutting my visits back to every 3 or 4 days because I will be back in shool full-time at the end of August. Also, I have 2 grown children living with me who need my time, too ( both have chronic mental health issues and we're working on building their support systems ) PLUS I have other commitments not to mention I'd like to take a break every now and then :)
Hang in there and I am certain other caregivers will chime in with their thoughts.
You need to draw boundaries with your Mom and be direct. "Mom, I love you dearly but I am unable to be there for you 24/7..." She just has to deal with your inability to give her what she wants.