We just got back from a Spring Break trip and we were at MK Thursday and Saturday and I nailed A&E both times (3rd in line, then 1st in line).
First things first, you DON'T have to be the first person at the rope for the pre-show and it doesn't matter if you're on the left or right side going under the train. One day we were on the right hand side behind enough people we could still see the welcome show. The other day we were on the left side behind about 3 groups of people and we couldn't see the morning show.
Once they "drop the rope" and people start moving ahead there are cast members who are "walking" and you have to stay behind them. So this is why you don't NEED to be at the very front for the opening show, because you literally have from the train station to the castle to catch up with the rope. Walk quickly and weave your way through people, if needed, to get as close to rope as possible. Try not to bump the person in front of you with your double stroller because I'm sure getting nailed by a stroller in your achilles is not a magical way to start somebody's day. While you have to be "determined" you can't be pushy. As I said, there's a lot of time for you to get close to the rope without pushing/forcing your way forward.
You want to be on the left side of the road. You don't want to be on the sidewalk. There is a ramp up to the curb at the castle and the person holding the left side of the rope walks through this so follow the person on the left to get up the ramp. 99% of the people at RD are going to A&E or the mine train. The other 1% are going anywhere else. Don't wait to see if other people headed toward A&E and then follow them or you'll be way behind. As you approach the hub the CM's at the rope will announce "those to Anna and Elsa follow me" and "those to Mine Train follow me". The Mine Train people veer off towards the Tea Cups and the A&E people go up the ramps and through the castle. Once you're in the castle walk on the left side of the hallway, try to be near the wall. When you get into the castle make the stroller switch. Tell the kids to get out of the stroller and one adult takes the stroller and the other walks with the kids. As you get through the castle they will announce "walk around the carousel for A&E". This is why you need to be on the left side because it's a bottle neck going towards the left, so if you're on the left side you'll be in front and if you're on the right you'll have to merge with everyone else. As you wrap around the carousel stay as close to the rope as possible. The adult with the stroller can run it over and park it and catch up with you either outside of the line or in line if your group is already in the building.
As you are walking around the carousel you have to walk to the left of the stroller parking, so everyone near the carousel has to go left causing a new bottle neck (this is why you MUST be to the left as far as possible from the time you enter the castle until you're in the line for A&E, there are two bottle necks where everyone moves from the right towards the left side).
As you get to the end of stroller parking a CM will announce "follow me to A&E". Get as close to that person as possible. That CM will literally walk into the line for A&E and then it's all single-file from that point on right into Fairy Tale Hall. The adult that parks the stroller will be able to walk past people in line to catch up with the family if they weren't able to catch up outside.
The key is to be left, be determined but not pushy, and to not wait for anything (this is why one adult parks the stroller and the other goes into the line.). If you have to park the stroller because you only have one adult then keep the kids in the stroller through the castle and park the stroller and try to get in line ASAP. But you won't be in the first 4 or 5 groups.