That's a rather intense flight schedule!
These are tips coming from a mom who travels alone with 2 girls twice per year. We have been doing this since the 2nd was 3 days old (long story there). It can be stressful, or it can be OK - it depends on your attitude & prep work.
Due to their ages, they will most likely do pretty good - as they get older they want to have more entertainment...
Check in online - Delta offers it within 24 hours of your flight. Print out your tickets & put them with your ID in an envelope in your carry-on. Makes things easier.
If your airport offers curb-side check-in, use it! The lines are MUCH shorter. Check your luggage here & go straight to security.
Make sure your tickets say "Infant In Arms" or "Infant" or "lap child" or something like that.
Depending on the TSA staff at your first airport, you may or may not be able to get through with pre-filled bottles of formula or ready-to-use cans. You are supposed to be able to take liquids for infants (one recently let my 5 yo daughter take a large bottle of juice stating that it was "for an infant")
Make sure you have bottles ready to go for take-off and landing - somehow sucking on the bottle helps with the ear pain that they feel.
Pack some books, a favorite stuffed toy (small) and a blankie.
Figure the amount of wipes you think you will need - then double it. My experience is that kids have blow-outs at the most in-opportune moments, and an airplane is one of those times!
Most airports now have family restrooms - complete with a changing table and sink - some even have toilets. Seattle has really nice family restrooms. Salt Lake has "baby rooms" with a changing table, sink & comfy chair - no toilet. Use these whenever possible!
On ling flights, don't be afraid to walk up & down the aisles with your kids. Many parents are afraid that they will bother the other passengers, but a screaming baby will be much worst than a parent walking said baby to keep them happy.
Security:
the laws just changed again Jan 1. We are on code orange as of 2 weeks ago (last time I flew). Make sure ALL liquids are in small (under 3 oz. containers) an inside baggies if you are carrying them on. It's a good idea to put them in baggies in checked baggage as well, but not for security.
They are supposed to allow larger containers for infants - i.e. similac ready-to-serve, hand sanitizer, wipes, etc. however, I would recommend the powder in the single-serving packets. It's just easier (unless you are nursing still - that's the easiest way to get it onto the plane!)
you are allowed 2 carry-ons per ticketed passenger - a purse/briefcase and a carry-on bag. toss your purse into a larger bag (i.e. diaper bag or shopping tote) and call it your purse. better yet, let your hubby carry the diaper bag & you carry a "purse" filled with books, toys, etc.
Don't over pack your carry ons. You will be lugging carseats, strollers, babies, etc.
If possible, see if you can get carseats provided at the other end. Carseats are not covered by the airlines insurance, ant they are usually damaged (just my experience). You have to sign a waiver that waives any claim you may have. Many car rental places will rent carseats, or if you are visiting family, see if they would mind borrowing aome from a friend, or picking up a less expensive set. Trust me on this one, it's just easier.
Are your strollers the smaller type? NOT umbrella strollers, but the lighter "around town" style? If they have a storage basket on the bottom, these are IDEAL. You can do plane side checked baggage - they take at the gate, put it on the plane, pull it off when you get off & you can use it in the airports to get to your connecting flight. DO THIS!!!
Even when my girls were getting too big to really fit & used the stroller to carry everything - the toys & blanket bag, the diaper bag, my stuff, etc. MAKE SURE that they will take it off at your next stop - with 2 babies, you will want it.
Now, for you & your partner...
Buy the largest bottle of water that you can find as soon as you get through security. Drink it. Do this again at your layover airport. Yes, you will have to use the restroom, but you need to stay hydrated on an airplane. You will feel much better the next day.
Delta & United now offer *real food* on longer flights - for extra cost. Plan on spending $10-$15 for an "on plane" meal - sandwiches, animal crackers ($1), etc.
Most airports have good food now. If you can wait (and have at least an hour layover) buy food at the airport & eat it on the plane. It's still pricey, but the selection is better.
Bring headphones. A pair for each of you. The ones you can buy on plane are $2, and not that great. Babies do sleep, and occasionally the movies are worth watching.
Bring a book for you too.
Above all, stay calm & don't let yourself get stressed - your kids will sense it & get... fussy. Most business travelers are parents - keep that in mind. They understand that families have to travel sometimes, and most are happy to help out.
If a woman who looks like a mom or grandma comes by on the plane & offers to hold the baby for you, she is just being kind. She has been there, and knows that you can get to a place where you just need a break. She's not going to take your child - where would she go?
The flight attendants (on smaller planes especially) are generally quite attentive the further west you are. It is in their best interest to keep your kids happy. They will offer cookies for the kids, water, etc for you. This is a good thing. If they aren't terribly busy, many times they will offer to walk your child up & down the aisles. This is a very good thing ;~)
Make sure that you walk up & down the aisles periodically - having a child in your arms is good excuse. You will need to stretch your legs on that long of a flight. This also helps for the next day.
If there is any possibility of having an empty seat nearby, find out. Flights are getting full, and in the winter they often cancel many, but there are times that it does happen. If you can find one, it is nice to be able to lay your child down occasionally.
Often there is an empty space right in front of the restrooms - this works well as an improvised play area too. Just stay out of the aisle and you should be fine.
One thing I have found is that flights that start in the western US generally have flight staff that is more... helpful. The further east you go, there are more people on the flights, and the the attendants are busier.
Generally, people like babies. Babies don't often kick seats. Babies are cute. a 3 yo, that is something else entirely... but with babies, people will understand that they are babies & need extra attention and grace. People understand - especially if they have kids of their own.
Have fun! Enjoy seeing the sun for a bit... we just went from Seattle to Ft. Lauderdale, FL for 5 days... it was a nice change of pace. I will warn you though... if you have any layovers, be vigilant on checking that your flight hasn't been cancelled. With the storms blowing through everywhere, they are randomly canceling flights just in case there is an issue.
I hope this helps!
J.