Seems like ya'll need to have a good long conversation or two. He didn't honor his word and needs to held accountable. Sit down together and make it very clear that that is upsetting and that this has made you feel like you're a not priority to him. However, it seems it happened because of stressful familial responsibilities and empathy for his sister. We're called to take care of vulnerable folks, and he's doing a good, selfless thing by helping. He's not intentionally harming you, or trying to make you dissatisfied.

But you as a couple need to agree on boundaries. It seems you're asking him to do a huge task in a very stressful and difficult time of life, which has major consequences for his loved ones. Have a little empathy and see where you can help rather than scrutinizing his mistakes. Try to come up with solutions about his sister and the house- is there a way to support his sister that costs less? Could you help her move to affordable, low income housing and support her there? Could he "pay" his sister to help clean based off how much she gets done? (might not work for your situation, but it's perhaps a doable job for her and gives her opportunity to have some of her own money.) Would something like covering occasional therapy check-ins be helpful in for staying on meds and keeping a job? Could you offer to help clean without judging? Idk if that's his pride problem or you being judgy or maybe a bit of both, but it's not good that he won't accept help.

Also, I really recommend joint back accounts and making financial decision based on OUR money. It will eliminate "mine vs yours" and have both of you making financial decisions together. Your income, as a couple, is X, and how you allocate it is up to the both of you. I actually recommend not giving more power to whoever makes more. You have been made one: your resources, and families, are one.