M.S.
I live in a remote part of Alaska, so I fly with my kids all the time - often times w/out my husband. My kids are 2.5 & 1.5.
Here is my advice: use rolling luggage and backpacks if possible. Have your older child bring his own rolling carry on. Pack it with 'special' toys & snacks. put just a couple diapers and wipes for the baby in the outside pocket. This is the bag that you should put under the seat in front of your son. If you don't already have a rolling suitcase for him, there is a nice quality one for $18 at Wal-Mart. I always pack extra clothes, diapers, and wipes in my carry on.
I would suggest having your fiance drop you off (even though he doesn't think its a good idea, it really will be easier). You can rent a cart while he waits in the car with the kids. Just walk inside and sit down at the first chair you see, your fiance can meet you there. The kids should be entertained by all the excitement of the airport!
I think the most stressful part of flying is getting thru security. Put your kids shoes and coats IN a carry-on before you get to the security checkpoint; and don't put them back on until you are totally clear of the security area. That way you don't have to juggle all the little stuff.
Remember when traveling with kids you ARE allowed to take milk or juice thru security. Also, if your baby still drinks a lot of milk like mine do; make sure to buy a few small cartons before getting on the plane. Lots of planes do not carry milk.
Finally, if you can avoid taking the car seats, that would help. We always try to borrow from friends or family when we get to our destination; or rent them with our rental car.
Good luck and have FUN!