I have learned alot about going to the parks over the last few years with kids...mine are currently 8 and 6. I have not used a stoller since my little one turned 4. Before that we rented a double stroller and I often only had one in there at a time. I would not recommend the rented stollers for those under 3 ...they can get out while you are walking!(Except for the strollers at DS) We employed different tactics with little ones but a backpack and single stroller worked well and then a single stroller and the leash on VERY CROWDED days.
I go often with just my girls( DH job takes him out of the country alot) and we always start our day early. Breakfast and cartoons in the room and to the parks to see the opening ceremonies. We have done so much without having to trip over others that by the time it gets crowded we have lunch and head back to the hotel for a swim/nap. After that we go back to a park for evening. We have done the parks all day, in the heat and we quickly learned it wasn't worth it. Everyone gets cranky that way!
I also head to quiet, less crowded attractions if someone starts to get cranky...some a/c...a place to sit...and a snack always rev them up again.
MK I like to ride TTA a couple of times without getting off (my 6 year old still takes a power nap on there!) and then go to CoP. The combination is fun and relaxing in the midst of overstimulation! At EPCOT you can find a lot of quiet places to duck into ...Just depends on what you like...we like UoE but that may scare very young ones. AT DS we like to duck into Muppets for a break and at AK you best bet is to find a quiet area to watch the animals for a bit.
I still find the hardest part of the day closing time. STAY PUT until the crowd clears out after the shows. It is worth the wait to not be in the crowd. But if we do get into that situation I hold onto both by the hand with one in front and one in back. They dont want to lose me so they dont let go and anyone that tries to break between us gets the evil eye and or elbow in the ribs!
The rest of the time you will see me (and this has been for 2 years )with 2 very happy girls in flip flops...yes, flip flops...skipping about 5 feet ahead of me heading for the next ride. I don't stress, we stop and do what THEY want to do as much as possible...even though there are a few things they have to do for me
Do what you can do and enjoy the parks...they aren't going anywhere and you can come back again...even if it takes years. My girls are at an age when they wonder why people get cranky and yell at their kids in the parks..my favorite line was when my youngest wondered why a mommy was yelling so loudly at her little girl and my older one responded loudly enough for many to hear " Because she didn't take her nap today!" She got many chuckles from nearby adults.
All in all the most important thing is to relax, take breaks and HAVE FUN! Enjoy the times your kids interact with CMS and characters...they are the best memories along with eating ice cream and ending up with it everywhere...who cares? Let them have fun and get dirty. You will be richly rewarded if you relax ....and so will your kids! Laugh alot, sing, dance and enjoy the Magic.