If you are talking about Spring 2023 you need to make a decision quickly. Interval deposits less than 60 days prior to use are restricted. Earlier is (marginally) better. RCI considers a deposit “not late” at about nine months; less than that trade power is reduced.
You probably also will need to be realistic about what is possible. You are trading off-season/shoulder season weeks but are locked in a school schedule where trade power required is likely to be at least moderate, especially for the more in demand resorts. In some cases, you will not be able to make a one-for-one exchange into the resort/time you want.
RCI is exclusively weeks, not partial weeks. (That is unless your ownership is eligible RCI Points, and it probably is not). I think II has a partial-week exchange system, but I’ve never used it.
I’ve been using both. Domestically, RCI has more inventory (and therefore more choices), but II has more of the nicer resorts and is a bit less expensive. (I am not sure about volume of international destinations in each system.) The ”resort quality” In II is a bit of a mirage, because Marriott and Sheraton both have an internal preference period, during which most new deposits can only be taken by another owner in that system. It sounds like you don’t own one of those, and it does make a difference. That doesn’t mean you can’t get resorts in those systems, but the more in-demand locations/times in those systems are probably going to be very difficult even if you had great trade power—and you don’t.
RCI has some features that might be helpful: for a fee, you can combine two (or more) deposits to trade for “better” weeks. It also allows you to get “change back” from a trade that didn’t require all of your trade power, and that “change” can be used for another exchange or recombined with yet another deposit, and so on. This makes trading even more expensive—the fee to combine, plus you are trading (part of) two weeks for one, but a three-for-two exchange might make a lot of sense for you depending on how much each of those quarter share weeks cost. RCI’s trade power evaluation system is transparent, so you know what each deposit is worth, and what each exchange might require. RCI also has a “deposit calculator” which will tell you how much a potential deposit would be worth if you made it that day. Those values can and do change with time.
In contrast, II has a feature that is also helpful: you can search against a week you haven’t yet deposited. This will let you see what II can do for you only for the cost of joining, and without committing a week to them. So, while it isn’t as transparent as RCI, you can “test the waters” a bit.
So, I think my advice is: join both RCI and II for now. Deposit your two spring weeks right now to RCI, and play around with it to see if they can individually get you something you might want, or if you’ll need to combine them. Use II’s feature allowing you to search without depositing to search against your Fall week to play around with what *that* system will give you. Then, adjust accordingly. No matter what, there is going to be a learning curve, and it will be very specific to what you own and what you want, so there is a limit to what someone else can tell you vs. what you can learn by experience. For me, that’s part of the fun, but I think I’m wired a bit backward.