I would say definitely do the Disney parks as well as Universal, i’m certain a 12 and 15 year old will still love them.
If you so stay in a (non Disney) hotel then have a look at the public buses. Most hotels in international drive, Lake Buena Vista and the likes will run free shuttle buses to the parks, but sometimes the times aren’t the most convenient. Public buses are cheap and many will stop at Disney Springs or magic kingdom and from there you can get on another bus to whatever park you’re going to.
I would also make sure to get fast passes for the rides you and DC are most excited about - you can book these online on the mydisney app so you don’t need to queue as long. Also if there’s any restaurants within the parks you want to have dinner in, also worth booking in advance.
10 days has worked for us in the past:
Magic Kingdom on first and last full day, Epcot, Animal Kingdom, Hollywood Studios, a Disney waterpark (personally prefer Typhoon Lagoon), Universal, a day at the pool with Disney Springs that night and then a day at the outlets shopping. We’ve been several times though so could be more selective about what we were doing/ seeing.
Never been in October but it will be all done up for Halloween. Universal have horror nights on - maybe worth checking that night out if it’s up your alley.
Finally - please don’t go to SeaWorld, those poor poor whales, it’s really not worth it.