The OP's trip would be a horrible use of the Scouts service if you ask me and I don't think they would be of much help to her, because what she is requesting isn't their primary function I believe.

Here's what my wife did when traveling with two little ones in a double stroller and it worked great.

1. Upon arrival at the airport, find a Porter to escort you to the ticket counter. Tip accordingly. $3 - $5 should be plenty.
2. Check-in your luggage at the ticket counter. Only carry-on what is absolutely essential to keep your little ones happy, occupied, and you sane.
3. Whatever you will need to have with you on the airplance, place in a small bag that can be placed underneath your stroller.
4. Whatever else you will need on the plane, place into your carry-on luggage that you can carry on your shoulder. A purse or a back pack would be great.
5. When you arrive at the gate waiting area, request a luggage tag from the gate agents in order to gate check your stroller.
6. When boarding begins, get in line promptly as you and your children will be allowed to board first.
7. At the end of the jet bridge, collapse your stroller and leave it. Ground personnel will ensure it is placed on the plane. You do not need to stand around waiting for the ground personnel to make sure they see your stroller. I promise, they do this on nearly every flight, every day.
8. Find your seats and place your carry-ons under the seats in the front of you. This way you will have everything you need with you and will not need to get out of the aisle to open the overhead bin. Trust me... this will save you a lot of hassle.
9. Upon deplaning in FLL, wait at the bottom of the jet bridge for ground personnel to return your stroller. Your stroller will be one of the first things they take off the plane.
10. Place kids in stroller and head to baggage claim to find Daddy.
11. Everyone will be excited to see each other. YEAH!!!

Good luck and have confidence that you can do this by yourself. Thousands of parents have before you and you can save that $50 for a nice date with your husband.

Have a great trip!