Strategic sickness...... Seriously I was once in a job with a near impossible workload. My predecessor took me out to lunch as suggested I went off sick for a couple of weeks. Only when bosses had to cover would they realise how much there was, would they listen. I was too honest, but he was right.
One approach, depending on family dynamics, might be for your husband to write, quite formally, to your step brothers. (Its what we may do if caring for my mother becomes too much for me. It would mean that any conversation is one step removed and so less chance for emotions/hfamily history to come into play.)
So, your DH is concerned for you. You have a lot on your plate and this has been gong on for quite a while. You have both given it some deep thought. The move is a good time to review things. You have been advised (no need for detail but imply that the GP has given you a clear warning to reduce your stress levels because it is triggering something nasty) to cut down where you can, and you will not be able to oversee this. You will also need one of them to take over as first point of contact with the various agencies.
You care for and respect your DSM deeply and would want to continue to visit and help where you can. However with other priorities including your DF, you cannot continue to be primary contact for your DSM. Could they let you know who will take this on and you will provide contacts and details of where things are.
The stereotype is that men expect female siblings to be carers. So the tone might be a bit man to man protecting his female. The content should be clear, constructive and reasonable. You have already decided you cant do it all. You could write the letter, but somehow we feel, given recent and even childhood history, that if we need to, it will be less messy coming from DH.
Then lie low. Offer perhaps to help with packing, unpacking but actually better to take a break and allow yourself some time to enjoy your family, see your father and simply do nothing. Indeed in the short term it might be better not to visit so you don't know about lightbulbs, and if anyone phones, simply and quickly tell them to phone your DSBs. I think you will find you are tireder than you realise, and the relief at not having to worry about phone calls is huge.