Staying onsite is the best. Especially when you find a resort you really "click" with. For me it's All-Star Sports (I'm a bare-bones type of gal)! The All-Stars offer convenience and value. If you're like me and rarely spend time in the room, the perks would be transportation, shipping packages back to the resort, a decent cafeteria, gift shop, a pool (if desired), and access to all the parks and Downtown Disney. If I'm feeling like I want to "splurge" then I go to Port Orleans Riverside for the atmosphere, quiet, and jogging trail.
The $14/day to park isn't worth it sometimes. I'm a passholder and have been getting great rates on rooms the past few years. You can't beat $59-$89/nite on WDW property!
Disclaimer: I'm a single FL resident. I have no idea the amount of time, money, and energy that goes into planning a family vacation. If you can get an awesome rate offsite during peak season and the costs versus benefits of staying onsite during your stay works out, go for it. BUT if you plan on being AT WDW during the majority of your stay, you might want to stay onsite for the convenience of being able to quickly go back to your room when it's the kids' naptime or if your health demands it.