Scampi, I'm so sorry to hear about all you are going through. It is really tough. I know you can handle it though, even if you feel you can't. The fact you are talking about it means you will be able to find reserves to keep going on.
I endorse what others have said...do start the Mtx. You will start on a low dose, and the folic acid you take with it will help sort any nausea. Let your doctor know what you are going thru, so hopefully they can support you too.
My Dad had Parkinsons. He quickly became too much for my mum to look after, and although we found it really hard to accept, he had to go into a resthome. This is something you, too, probably won't want to hear. But your Dad has his own health worries, and taking care of your Mum may be just too much worry for him to handle. It is scary being around Parkinsons sufferers, as they are so fragile and they fall so easily. Dad had some horrific injuries from falling, and was in and out of hospital as a result. He had an emergency bracelet but the damage is done before the ambulance gets there. Parkinsons sufferers need help so they don't get into these situations in the first place. They need input from physios and occupational therapists. I tried to get them to accept live-in help, but they were against it. I can understand it...strangers in your home. But it would have allowed him to stay at home longer. In the hospital they often played around with his meds, which would then create hallucinations. We finally had to say "no! don't touch a thing, leave it alone!". Parkinsons sufferers need their meds given to them at exact times of the day. They need a high level of care. Can your father do that? Particularly with his medical conditions?
You may not want to hear all this, and you did say you wanted to just off-load. I understand, and I apologise if my input is unwanted. I hope you have someone supporting you, so you can support your parents. I hope there are other brothers and sisters who can share the load and help your parents cope. You all need to sit down together and work out a plan. For everyones sake.