Christmas casual is definitely doable - just make sure you're on top of your manager giving you shifts you can do. At the end of the day, you're casual - they have to work to your schedule. That doesn't mean they won't try to bring you in when they want (as opposed to when you want), but unless your manager or whoever is in charge of scheduling is a right arse, they put you on the days you say you can do.
And if they don't, and you don't show up because you can't do that shift, what's the worst-case scenario, they fire you? Like, that might sound bad at first, but if they fire you, all that happens is now you're in a position where you have only a part-time job and no casual job - which is the same position you'd be in if you don't apply at all. Firing may seem like a bad thing, but if you think about it, you don't really lose anything by being fired for not being able to match their schedule, if this is the one thing putting you off applying anyway. Even then, firing isn't going to be first response - they'll write you up first, give you warnings, etc. etc.
But again - if you're on top of them about what shifts you can and can't do, and give them plenty of notice (preferably in writing in case they try to make the claim "you never said that" later), you should be fine and this shouldn't happen. Plus, even if they do try to give you a shift you can't do, don't forget you can always try swapping shifts with others - usually easier said than done, but still an option. Also don't forget you're allowed to knock back shifts if they ask you to come in at the last minute and you're at your other job - a lot of casuals don't because they want more shifts and are scared of not getting some, but you already have a part-time job anyway, so you're likely going to have a fairly full week even without the extra extra shifts. I think most places are aware that many casuals double up over the holiday period, and I had a friend once who tripled up, so they likely won't complain about it as long as you're still doing shifts to help them out with.
One thing I'll note, though - you making extra money isn't likely to help your parents with being able to get a house, unless they're loaded and actually want to buy it outright (to which I'd add, is your meagre casual income even going to be able to help with that?). They'll be looking at getting a mortgage from a bank, and most banks aren't even going to pretend to consider a teenager's (or 20-year old? Just guessing) casual income. The part-time job they might, since it's a little more secure - but not a casual, because you could lost that income at a moment's notice by way of your employer just choosing to not give you shifts. Still worth applying for a casual Christmas position, but just be aware you likely won't be as helpful to your parents as you think you will. It's a nice thought, and somewhat admiral of you (I wouldn't work that hard just to give ALL my money to my parents, that's for sure), but probably not that fantastic, sorry to say.