And OP: Offsite is worth considering! It is not exactly the same as being onsite, but we found the two to be much more similar than they were different. We could usually rent a 2BR condo plus get a rental car and pay for theme park parking for about the cost of a single Disney Moderate room.
In other words, there are three things that a family might want in their WDW lodging:
- To have a reasonable amount of space.
- To spend a reasonable amount of money.
- To be onsite.
For most definitions of "reasonable", most families can only have two of these three. For your family, "reasonable space" is a requirement, not an option. Space was also our biggest priority, because we enjoyed our vacations a lot more when we were not on top of each other and had the creature comforts of "home" in the unit.
So, at that point, you are deciding between #2 and #3. You probably can't have both.