Definitely bring your own stroller! We went last year with DD1 and DD2.5- having our own stroller was a lifesaver. Both girls actually were able to sleep in it and were more comfortable since it was their stroller. Plus, then you have space to store things underneath that rental strollers or umbrellas might not have. There are plenty of places to park strollers around the park and paths are wide almost everywhere. ALso, if you arrive at the parks early, you will find it much easier to walk to the entrance rather than taking the trams where you have to fold the stroller to sit.
Be sure and take everything at their pace or you are in for tantrums. If you can't return to your hotel for a nap, don't plan on staying 12 hours at a time. When we go again in two months with DD2 and DD3.5 we plan on no more than 3/4 days in a park. Some days we will do early mornings and leave soon after lunch, other days take naps midday and then return to the parks for late afternoons. It will keep us all saner!
Another hint- watch the Disney sing along videos ( Campground Mickey, Beach Club MIckey,
Disneyland Sing ALong, etc. ) They have the actual characters dancing and interacting with kids so your girls have a sense of their sizes. We found these GREAT before the last trip and have been watching them again in preparation for this trip. The girls love seeing the characters, singing the songs, and DD3.5 even recognizes many of the sights/rides from last trip. You can find them on Ebay or maybe the disney site.My DD2.5 was terrified of all characters (Santa, Sesame Place characters, etc) before our trip last year, but was in love with Mickey and friends- I am convinced that the videos were the key!

Character meals are great- just make sure that the girls have time to warm to characters first. We gave my DD2.5 the "job" of giving each character a "high five"- definitely helped her break the ice!
Other thoughts- take moments for quiet fun- Tom Sawyer Island, pooh's playground, running in the fountains, music/little shows- the girls will love that even more than some of the rides/big performances. Don't discount the potential for fear on the "dark rides"- my older daughter had more problems on It's a Small World and Pooh than Goofy's Barnstormer roller coaster- mostly because of how dark it was in there. This time, I will come prepared with glow sticks or mini flashlights for the girls to hold when the get scared.
Oh yeah- bring a spare change of clothes and socks- the little ones love playing in water and there are chances for this everywhere!
Finally, I highly suggest you take some time to enjoy a ride or two (at least!) with babyswap. DH and I picked a ride in each park we really wanted to do that the girls couldn't and used babyswap. It was great- so much of the trip was centered on their needs, but we got some thrills too. Plus, it is a good time for the kids to zone out with a snack- or maybe do the kidcot stops or kid stamp zones at Epcot and Animal Kingdom.
Enjoy!