Obviously, as you mentioned, you'll ask a specific shaila.
Here's a couple of issues for you to check out and ask:
1) how was your pool made? If it was a preformed concrete block which is placed in the ground, it might have "toras kli" on it (halachically called a vessel) which would make it pasul. You might need to undo the status of a kli by detaching it from the ground, puncturing a hole in the bottom so it wouldn't be able to hold water, and then reattach it. This would be a real pain to do with a hot tub!
However, most (though not all) in-ground pools and tubs are made from just pouring cement into the hole and attaching tiles. In this case, it's unlikely that anything had "toras kli" before attaching it to the ground.
(Shut Shevet Halevi and Minchas Yitzchak are both lenient regarding tiles, even if they have an indentation in the back to receive the cement, since they are meant to be attached to the ground.)
2) Is there a drain of any sort? You only mentioned a hole between the tub and the pool. Is there a drain in the tub itself? depending on how it is constructed and where it's located, that could also be a problem.
3) How would you plug up the hole? You don't want a plug which can be mekabel tum'ah. Plastic or rubber is usually ok, metal ones aren't. Some plugs also have indentations which could be problematic (a 'beis kibul' or a receptacle is called a kli) so you would need to check out how the hole is being plugged up.
4) How much water does the tub hold? The minhag is to have 1000liters (shu't cheshev HaEfod and many sefarim quoting him) though the actual shiur is between 750-850 liters. You need to check with your rav about it.
There needs to be enough space above this level of water that even when a person goes in, and the water rises, it won't spill out of the mikva.
(There's a preference that there should be a shiur of water below the hole connecting the pool and tub, such that even if the hole gets left open accidentally, there's more room to rely on the shiur beneath the whole see siman 201 sif 40-41.)
5) How is the water entering the tub? we generally want the water to enter after running on the ground at least 3 tefachim to accomplish "hamshacha" which removes lots of issues with the water. You want to make sure the area surrounding the tub is free of anything which could make the water pasul (i.e. it shouldn't hit any tools, or anything which has toras kli on it.)
6) You need to make sure the pool is entirely dry before any rain water goes in. That means after draining the water, you would go over it with towels and maybe putting heaters there to ensure it's dry. There's often a problem when concrete gets dried, but then afterwards "sweats" the water from inside it. So you need to check with your LOR how dry you have to make it.