Don't freak out; it'll be fine. I've traveled with my two girls at your kids' ages and younger, both with and without my husband's help, and they'll be calm(er) if you are.
My advice: Do everything you can to ensure your health and your kids' health before you get on the plane. Colds, ear infections, etc...make things a lot more difficult.
I think on most flights you can have kids under two as a 'lap child'. Since ticket prices are climbing, I would try this with the 14-month old (we bought a seat for our younger once, then didn't use it because she wanted to sit in our lap anyway).
Board last or almost last. Let them run around (with limits of course) before boarding, then when you get on the plane, it won't be too long before takeoff and they'll be tired and want to sit down. We didn't let our kids wander the aisle on the actual ride because of safety, but if your trip is long, you might have to.
I brought candies and treats for not only my kids (not the ideal snack, but this is special!), but for the people around us. I handed them out with a smile and apologies if my kids were whiny (sometimes they were, sometimes they weren't). Then people tend to want to help you instead of turning away :)
About the fluid--they made me dump out the water in my kids' sippy cups at screening, but let me take on milk and juice! So, since I knew my kids would be getting suckers on the plane, I took empty sippy cups through screening and filled them up with water before boarding.
Bring several toys that are new, borrowed, or been in stow for a while. Then the toys will be 'new' and more fun.
I recommend having an umbrella stroller; it's easy to stow and carry, and it'll help with a sleepy or uncooperative toddler. If your husband isn't with you, I would bring the double stroller if you have one (we don't, but I still did fine with a two-year old and a baby in the umbrella stroller).
GOOD LUCK! It'll be work, but will be worth it!