I was just trying to think of things that wouldn't cost money - like, going for a walk at home requires no gas money or anything. If you have a membership though - go for it! Hell, you don't even have to actually work out if you don't want to! Just have a shower there before you head home so that it looks like you got sweaty and showered. haha. Or go putz around in a bookshop or a coffee shop or something during that time and then pop in to the gym.

Oh! Offer to pick up groceries. Let your mom give you a list and the money, and you could take your younger sibling(s) with you as a "treat" for your mom to just chill on her own.

You could experiment with some simple recipes - there's loads of them online.

You can always do other chores that aren't in the kitchen - you could vacuum, or dust as that requires going room to room. Do your younger siblings have like a playroom or anything? Reorganize and tidy them if they do (or their bedrooms).

You could also volunteer to shovel the laneway if it snows and needs shovelled! THAT is a chore and a half that takes ages!

And with the younger siblings - Christmas movie nights are tooootally possible.

How old are your siblings? Could you do crafts with them? Those take up time, especially if you pick out some time consuming ones!

Is there any chance that you could get some knitting needles and attempt to learn how to knit? If you're just learning it'll take loads of concentration. If your mom is not fully up with that, say you want to try to make her a scarf (OR blanket! That'd take longer) and since you're just learning you really want to focus so that you could possibly see if you could finish it before you leave. Ask your dad if he'd purchase the yarn as a present for your mom.

I'm just trying to help brainstorm. I totally get how crappy it is to be stuck there, and if it's inevitable... can at least try to find as many things as possible to keep you occupied and try to keep you in spots where you can have minimal contact.