Compared to staying off property, all of these choices offer a dramatic upgrade for convenience.
We have stayed at both Yacht Club and Wilderness Lodge with children in your age range. We found both to be awesome and I don't think you can make a bad decision. If you are going to be very focused on being in the parks and do not plan lots of resort time, I'd point you toward Yacht Club or Beach Club. These resorts share facilities and Stormalong Bay, their pool which is the best pool complex on property. You will have walk-in access to Epcot and boat access to Hollywood Studios. All other destinations are reached by bus. Both resorts are great, we like the Yacht Club a little better and tend to stay there when staying Epcot area.
Wilderness Lodge is my favorite resort. The boat to the Magic Kingdom is not an issue with little kids, and if you catch one of the larger boats you don't have to fold strollers. You do have to fold on launches. The setting of this resort and the theming make for a great resort to explore. The pool is very cool and is surrounded by a geyser, waterfall and a view of Bay Lake. If felt the service at WL was a little more hands-on and we really like walking and exploring the resort grounds. People make a big deal about the fact that you are on boats or buses to get around, but we felt the transportation was great and bus times were relatively short with bus overcrowding limited.
Because it is walking distance from Epcot, I'd say the YC/BC is slightly more convenient in general, but some buses are shared among the two resorts and with Boardwalk, so we have on occasion chosen to take cabs back to the resort if we leave a park in the closing rush. This is not a requirement, we just have found it easier when leaving in big crowds and little kids when patience in our party is running low. Vans are always hanging around at park closing for schlepping back with larger parties.
I find these resorts are both excellent and are reasonably similar in convenience unless you think you will be spending the majority of your time in Epcot and Hollywood Studios. If we are planning on more resort time, we'd tend to head toward Wilderness Lodge. If we want to be in the middle of things and have lots of options and action, Yacht Club would be our choice.
And if it's a push, you'll save some money booking at WL -- not a bad bonus for such a beautiful resort.
Either way, have an awesome trip.