This might be a bit of an epic post, I'll try to break it down into manageable paragraphs.
Choice of hotels-
Staying in a Disney owned hotel would give you certain perks. Disney has a very good free bus service between their hotels and parks, and you'll get Disney park entry included. You'll also get Magic Bands, which are basically wearble park tickets that would also be your room key and can have a credit card linked to them. Staying in a Disney owned hotel would also mean you can make fast pass plus reservations before you leave home. Fast pass plus (FP+) lets you book a timed slot for rides which mean that you don't have to wait in a long queue. The whole FP+ system can seem baffling if you haven't encountered it before, and I strongly suggest that wherever you choose to stay you read up on it before you go (or PM me and I'll explain it) Unfortunately there is absolutely no way to avoid highly excited small children at Disney hotels. Disney buses don't run to Universal and vice versa.
Staying at Universal would give you a bus service to Universal parks. As far as I know Universal hotel guests get entry into the parks, and I think you also get Universal express passes, which put you into a priority queue line that moves faster than the regular one. While Universal is more aimed at the over twelves, and doesn't have the princess factor of Disney there will still be many small children at the Universal hotels.
Staying "off property", ie in a non theme park owned hotel is cheaper than staying on property, but you will lose all the perks. Most Orlando hotels run shuttle buses to the theme parks, but there may only be a few morning and evening not the continuous service you'd get at a theme park hotel. Of course you can always take a taxi or hire a car for the duration of your trip which would negate the need for buses. I'm afraid there will be many small children at off property resorts as well.
Avoiding small children could be done by booking a private villa or apartment, however if your accommodation had a shared pool as many of them do there will most likely be children using that.
Staying in a hotel outside of Orlando. One way to avoid too many small children, stay a bit cooler and have a few relaxing non theme park days would be to stay in a hotel somewhere along the Atlantic coast. That would put you about an hours drive from the theme parks, although you'd be very close to Kennedy. Of course there's no way to do that without a hire car.
Theme parks- (please forgive me if you already know what I'm about to write, but from your OP you sound like an Orlando novice)
Epcot is part of the Disney parks, along with the Magic Kingdom, Disney's Hollwood Studios (which may have a different name by July), and the Animal Kingdom. You can buy tickets that allow you entry into all four parks if you wish, or separate day admission tickets.
The Wizarding World of Harry Potter is spread across two theme parks, Universal Studios and its sister park Island of Adventures. The parks are next door to each other, Universal has Hogsmeade village and Hogwarts, Islands of Adventure has Diagon Alley. To visit both parts you need a ticket which lets you into both parks, or one day admission to each park individually.
Kennedy Space Centre is not in Orlando, it's about an hours drive away. For a teen it's a really good day visit, and a nice change of pace from the theme parks. I wouldn't recommend it for younger children.
I hope that helped, I've honestly only scratched the surface here, if you want to know anything else please feel free to PM me. Orlando and its theme parks is a bit of a specialist subject for me.