Don't have time to answer more ???s. But I have another myself and this may be insane on my part.
In looking over some responses, I have to agree I was kind of arrogant and stupid in suggesting things like an energy audit and so forth. Would it be okay if I just sent a short email apologizing for that gaffe? I had no intention of minimizing their problems by doing that. It was something someone else spoke about and I thought "Ooh, good idea. Maybe they have thought of it, maybe they haven't."
On the other hand, I disagree with my brother that he would have to spend "thousands" on appliances. Each appliance that I bought in the last few years
has been under $600. Of course-- I don't need or want a stainless steel fridge with all the latest doo dads, either. (And no, I would never say that to them!)
If I were you, I would apologize and then move forward. You really do need to work this out civilly.
"Brother, I'm sorry for suggesting the audit. I overstepped. I would, however, like to talk to you about a long term plan for taking care of Dad. While the current situation isn't working, I do think we can collectively come up with something that is fair to both of us and also be in Dad's best interest. I'm not sure that I'll be able to fly down there anytime soon, but what do you think about me calling you guys next week so we can all talk it out?"
I might send something of "My apologies - I simply thought you hadn't thought of it yet. Let's talk over phone/Skype soon. Love, Yarnspinner."
And then drop it. I would have the real conversation over the phone or Skype with just your brother or your brother and father. No reason for SIL to be in on the conversation, even if she is married to YS' brother. I know others will say that they're married and finances are co-mingled, but SIL needs to step back and let the siblings deal with their father for a moment.
It's not just that their finances are comingled. It's that he's living in her house. Not only is she contributing financially, in part, but she is also dealing with the day-to-day activities associated with him living there. It wouldn't be fair to tell her that she has no stake in the claim when the decisions made very much affect her, her home life, her finances, and her kids' lives. Now, if there's animosity between SIL and OP, it might be wise for her to discuss things with her husband and then trust him to represent her interest, but I don't think anyone should say that this is just between siblings. Dad is only going to need more pointed and deliberate care as he ages and she very well be the one that chauffeurs him around, cleans up after him, deals with emergencies, takes time from doing things with her kids to care for him, etc. She very much should be part of coming up with the plan and her input is just as important as either the OP or her brother.