How about the big stroller for the 2 year old and an umbrella stroller for the 5 year old? Because even 5 year old kids get tired of walking around Disney and can use a break. We went in Feb with our then 3.5 year old and we had the big single-child stroller for her, and it was totally worth it. DH just wanted an umbrella stroller but it was nice having the basket underneath for carrying stuff (I had a back pack too but usually it had to come off for rides and then it just went under the stroller). Actually, we totally lucked out, in that we were staying off-property and happened to find a thrift store that had a stroller for sale for $10. We snapped it up, used it for the 10 days we were there, and then donated it back when we were leaving! Best $10 we ever spent!
As for the other part of your question, you will definitely want to do a mid-day break. Get to the park right when it opens - be there for the rope drop. It usually isn't that crowded yet and you can hit the most popular rides first without much waiting in line. It starts getting a lot more crowded around 11 am or so and the lines get much longer. Around lunch is a good time to take a break, head back to the hotel, swim in the pool, take a nap, whatever. Then everyone will be much more refreshed to head back to the park for more rides, evening shows, etc.
And use Fast Pass wherever you can. And pick up the Unofficial Guide to Disney World - they come out with a new edition every year and it's proven invaluable every time we've gone! Good luck and have fun!