I think you need a break, so try and fix up respite care so you can get away for a while.
Why are you helping your daughter with child-care, instead of her helping you look after her father or step-father?
We can all of us only do so much and feeling tired or resentful all the time only makes it harder.
A lot of men (most of them) react to adversity by being grumpy.
Reading your text I think we all felt at first sight that your husband has every right to feel grumpy, being grudginly helped be a wife who resents him, but you probably didn't mean your post to come across like that - you are just at the end of your tether.
So my suggestions are:
Respite care
A straight talk with your daughter asking her to help you, or at least make other arrangements for child-care
Find a dog walker to take the dog for a long walk every day, and you can still take it for shorter ones to get out of the house
Find someone who will come in for two hours once a week, so you can get out and do whatever you like for that time.
My mother was a right pain in the a* for the last three years of her life and we all, my father, my sister, the home helps and I exploded or broke down in tears at times. And we all knew the feeling that we just had to get out.
Rain or shine, I rode my bike for the hour that she slept in the afternoon, just to get away. So I know how you are feeling right now.
Sit down with your husband and tell him that you just cannot cope with looking after him, the house, the dog, the cooking and cleaning all on your own.
He may not like the carers, but you need them coming in regularly.
If you can afford it, get a cleaner too and send the laundry out, if no-one will come and do it for you. Otherwise bung it in the washing-machine and then in the dryer and don't iron anything!