Kind of a tough call due to the length of your trip. Also not entirely sure what you guys will enjoy doing or your budget for the trip.
To answer your one questoin... SeaWorld and the Universal Parks are about 20min away from Disney, just up I-4.
Despite my love for being offsite and the freedom a car gives me, As your first trip, and a small family, I'm tempted to tell you to stay onsite if just to avoid the need for a rental for the 2 weeks, or the need to learn and familiarize yourself with the surrounding area. (Disney is big enough, no need to force an information overload learning more around the area).
A couple possibilities for you might be to look into renting
DVC points for a stay in a small DVC unit. It'll give you a bit more space than a value room to spread out, plus a kitchen area which you can use to prepare breakfasts in the AM before visiting the parks, or to store and reheat leftovers. It might help make the longer stay more bareable than a full 2 weeks stuck in a small hotel room.
Another thing that might be worth considering if you think you'd want to check out the Universal parks, would be to start your visit onsite at Disney, and then for the last 2-3 nights jump over to onsite at a Universal Resort (You'd either need to rent a car for the move, or get a taxi). Then you can relax around the Universal parks and their REALLY nice hotels.... plus get a change of scenery from your Disney stay.
As someone mentioned previously, We are more than willing to help provide ideas and suggestions to plan your first Disney/Orlando trip... It just takes a bit better idea of what you are wanting to get out of the trip, when you are planning on going, and what your budget looks like (Small? medium? large?) so that we can give more tailored suggestions to suit your needs/desires.