I'm guessing you're not going to want to hear this, but...
Seats that are checked, even gate checked, are as good as crashed. The airline makes no guarantee that they won't (for example) drop them from the jetway where you leave them to the ground for the ground crew to put them on the plane, or otherwise mis-handle them.
I'm also not a fan of lap babies on planes -- if my purse needs to be stowed safely under the seat in front of me to prevent it from being a projectile and hitting someone in the head, a baby (or toddler...) isn't safe on your lap, either. I also believe that the airline "lap child" policy extends only to those UNDER 2, so your 2 year old may be required to have a seat.
If you have decided that you are going to travel this way anyway, I'd look into seeing if your LA friend can get/borrow etc. reliable carseats there, so you're not subjecting your seats to abuse on the airline. Ideally, purchase a seat for each passenger on the plane, install seats on the plane, and use them at your destination.