Are we eligible for respite care? And if I'm qualified to do it, can I get paid to take care of my DD/MR son?

My son is ten years old and has Cerebral Palsy, Profound MR, Epilepsy, a G-Tube (to eat), and is 100% incontinent and immobile. Needless to say, it is extremely hard for us to find a sitter when we need to run errands and whatnot. People tend to be extremely intimidated by his condition and even his extended family members won't watch him... ever. It's really hard for him to comprehend why his aunts and uncles come over to pick up his older brother, but they never take him. So, since we are here with him all the time anyway, and his biological mother isn't working for this reason, is there a way that she can get a waiver or be employed by a respite agency to stay home with him and get paid? Not having a dual income is causing stress on our family, and I (mom's girlfriend of 5 years) am the only one able to work because she can not find anyone to watch him so that she can work also. The boys' dad does not pay child support, even though he has been ordered to by the court system, and he only takes the boys every other weekend. Does anyone have any ideas for us? We would really appreciate some honest advice to help get us out of this rut. Thank you very much!