Caregiver

For months now my sister and I have been helping my dad care for mom.  She has dementia.  My dad does the best he can but, being a man who has never had to "care" for anyone else and for the length of their 65 year marriage was cared for by mom, he's in unfamiliar territory.  It took us a couple of years to see just how much help he needed and we slowly started insinuating ourselves into their home, first cleaning it, then taking mom to get her hair washed and set, then bathing her, then helping out with meals. 
Dad has his way of doing things and it doesn't occur to him that they may not be the best way of doing things for mom.  For him, it's the most expedient way.
And he's tired.  He has is own health issues and not a lot of sympathy.  His sons are less than sympathetic because they don't like how he "treats" mom.  Guess they don't know that ol' walk a mile in my shoes thing.
Well, Wednesday morning, he slipped in mom's shit (she wasn't wearing her diaper) and fell and fractured his hip.  groovy.  Thursday surgery went very well. 
Sister stayed the night with Mom and we put together a schedule of 24 hour shifts for Mom until....
Brothers and older Sis are hell bent for leather to get in professional help 24/7 so sister and I can get on with out lives.  I'm fighting this but am not sure why.  I feel like we're betraying our parents.  So, they have the money to get help.  That's not the point.  My brother is living in statistic land.  No child can take care of their parents. It just doesn't work.  Being who I am and where I come from, my hackles are raised and I aim to prove him wrong.  At least until I can't do it any longer. 
Why are they so het up to not let us help?  Why can't they just leave us alone if they don't want to help?
I don't want to spend my next few months or years caring for old people.  I cannot fathom not helping as long as I can. 
I have the full support of my dear husband.  My children are grown.  I've always been a caregiver.  It's what I do.  And it's not forever.
I can't shake the feeling that they want to be as far away from this problem as possible and if sister and I are involved, they'll feel guilty for not helping?  Then they can go off and be mad and what....
I guess they don't know the feeling of helping someone who has always had your back, always loved you, always been there.  How can I abandon them?