My parents are 79 and 83. My mother is my dad's caregiver. She is stressed. What kind of help is available?

If you parent would like to be together at home but need assistance look for a livein caregiver for both your Dad and to help your Mom out. Start at your church or local Hospice. Your Mom might like the company and help around the house if they have a long term insurance police it might even pay for these services. I am caring for a female right now from my church. Her Longterm health plan pays for someone as long as it is not family to do most everthing from shopping to care which also covers companionship. Someone doesn't have to be a nurse but if they are caring and can work with your Mom to learn her likes and way she does thing it will be a win win for all. I have been helping friends and family for over 6yrs now. It is on a just give me a call and I will be there. One day at a time.
Good Luck and God Bless

Without knowing both your Dad's health and mobility issues, it is hard to say whether he needs an asst. living facility or NH. I would try my best to keep him out of a NH if you can. ALFs have so many services now and have a "tiered" approach to care. So you may want to start there.
If you feel he needs more medical care and help with ADLs, contact his doctor and ask where to begin with your NH search. Also, look online for evaluation sites...Medicare has one too.
Do you have your parent's Power of Attorney? If not, you need 2: one for financial, one for medical. You may also want to get a medical directive for your Dad which spells out his wishes if he becomes incapacitated.
If you decide on a NH you have to decide whether he will do private pay or if he is eligible for Medicaid funding. This type of planning is so important and you really need an elder attorney who specializes in Medicaid.
If your father or mother was a veteran, there are also benefits. The VA website has this info. Again, your attorney can help there too.
good luck