If you can, buy an umbrella stroller (around $20 - $30) at the Wal-Mart in Orlando. If you are stopping for groceries, Wal-Mart has those too. If you are going to be in WDW for any length of time, you'll save money. The umbrella stroller with help with your 4-year-old, but not the 7-year-old, but if you've done any walking in preporations, (s)he will be fine.
You can use the stroller outside the parks as well. Umbrella strollers fold-up nicely, so even when taking the bus it's not too bad.
Good luck and enjoy your trip!!!
Lori
6/1997 Off site, 2/2000 Off site, 2/2001 Poly, 10/2001 POFQ, AKL & Magic, 1/2002 ASMo