I think you need to direct your anger elsewhere. You should be furious with your mother and sister for descending at the last minute. They are the ones who deserve your ire, not your Mil or your husband. Your MIL did her best to be accommodating, your husband clearly didn't want to change the family plans, thought of the trouble his mother had gone to and quite reasonably in my view expected that you should stick to what was organised. And your mother and sister turn up out of nowhere and upset other people because they don't make plans!. Well, in my view they are selfish and thoughtless and you should be mad as hell with them for not being willing or able to get their act together
This. ^
Your mother sounds like a rude, toxic, selfish, self absorbed narcissist, thinking the world revolves around her. Sitting at home on her own is her own fault and serves her right. It's a direct consequence of "not being a planner". That's all about control - thinking she can just do whatever she wants, whenever she wants and that everyone else will fall into line.
Your DH did the right thing in refusing to cowtow to her and in wanting to stick to the original plan. Your MIL handled herself very well, by offering to change plans, something she didn't need to do.
Your anger needs to be directed fully at your mother, not your husband. I'd be furious too if I'd offered/planned to cook a meal for my in-laws and then they wanted to change the plans (again!) by taking only my spouse out for a meal instead.
Is there a reason you're so desperate to fall into line with your mother? She doesn't sound worth the effort TBH.