My first thought was that your husband and his family are entirely too immeshed in each other. The extent to which your husband takes offense at any perceived criticism of his family is ridiculous. As is calling his parents in the middle of a show at Disney World.
I find it interesting that counseling is so forbidden but that it seems the family is accepting of your SIL getting the help she needs. Frankly, I don't think it should matter if everyone else thinks getting counseling means you are a raving lunatic. You and your husband need it.
If he won't go, then you go. You feel guilty for being moody for a little thing compared to him. That's just a minor version of what you say he is doing - feeling guilty for having fun when poor mom is suffering.
You need to see someone who can help you set some boundaries and have a voice in the relationship (like your indicted BIL handling your financial affairs. Holy Moly!!!) His moods shouldn't dictate your whole family's lives. When he decides to pout for months and months, then you need to be able to say, "ok. But the kids and I are going to live our lives and do X, Y, and Z and enjoy doing it." THen do it. Live your life. Stop asking if he's ok, if you can fix it or do anything for him. Tell him you are there for him if he needs to talk but let him take responsibility for his own behavior. You can't follow him around trying to make him be happy.
Also, not that it matters, but I think moving to be near his family is a terrible, horrible, very bad idea. If you think it's bad now...just wait. I would bet your husband will practically live at his mother's house. Besides that...is this a permanent move? Since her illness is chronic but not soon to be fatal...you are going to be there forever. She will never be "well enough" for you to move back. I think you need to be prepared to accept that you are moving there for the rest of your life (because after mom dies you will have to stay because his father/brother/etc. need him). And, you will need to accept that you will never be as important as they are.
One last thing...I get that his "old fashioned" parents would find counseling objectionable, but who has to tell them. Will your husband refuse it as well because of the same reason?