I imagine lots of us have had these pressures. You feel pulled in so many directions and seem to have so little time for yourself.
Is work necessary?
Not having to work would free up some time but I daresay your family responsibilities would increase too.
Work can be a bit of a haven too, where all you have to do is concentrate on your job, and have some adult company.
There are no answers really.
This is a stage of your life where you have to juggle your responsibilities, and make time for those you care for.
It's frustrating and tiring and involves some guilt too.
The light at the end of this tunnel is you grow older, children become easier to care for as they grow up...but you'll lose your mothers, and as the years fly by (and they do,)you'll be the ones looking to family to assist you.
The circle of life, which at times is very difficult - when family is a joy, a blessing but quite often problematic too.
Sounds like you need more time to deal with family matters, and to have some quality time for yourself too, so something has to give. If time cannot be found you have to stretch yourself the best you can and just deal with it.
I often thought of running away when life felt so demanding
I didnt.
I'm older now, but family problems and worries of one sort or another still remain.