Welcome Cherry. Something clicked in my head while reading your post, and I just thought I'd throw it out here. There's a woman in my church group, about 60. She has raised all of her own children (5, I think) and is now raising many of her grandchildren. She babysits children all day every day, even on weekends (a different set of grandchildren then).

The thing I've heard her say on many occasions is that she has never had a vacation...even to attend church or her monthly church group meeting, she has to go through what she calls a 'hassle' to get her son to find someone else to look after the children for those few hours. She says she feels like a prisoner, trapped in what she calls a "drudge life with no end in sight".

Your Mom probably isn't feeling that gloomy, but her words "just getting away" are a big clue. Maybe she feels the need for a week or two off just for some R&R. Is there any way you can get her to elaborate what she envisions when she talks about moving or just getting away? Have an honest discussion with her - maybe she just needs a few days to herself but won't ask for it because she knows it will create hardship for you.

Are you vocal in your appreciation of her for looking after your children? You'd be surprised how many children don't think to verbalize their appreciation to the parent! My friend at the church feels used and abused...her children don't even ask her out to restaurants when they go, or think to ask her if she needs help with groceries (and how can she go shopping when she's looking after children all day every day!) They rarely say thank you to her. That ongoing pouring out of oneself without hearing any expression of awareness or appreciation for the effort and sacrifice can be very demoralizing.

Again, perhaps none of this fits your situation. I'm just passing along what this other woman's experience has been. If you could just get your Mom to open up and find out what's behind those words "just getting away", you might be able to find out more of what she's feeling.
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When you don't like a thing, change it.
If you can't change it, change the way you think about it.

(Maya Angelou)