I've moved flying on United, with a 2.5yo kid and a cat.
There are only two red flags that I see.
1. The foldable highchair in the stroller bottom basket. Unless the basket is sealed you should worry about the possibility that the highchair will fall out as UAs baggage handlers move/toss the stroller around.
2. The diaper bag would be a problem if it's not actually used for diapers. But diapers for a kid that uses them on the flight + other stuff should be fine.
I also noticed one possible way you could bring more stuff. Are you buying a seat for any child? If so, keep in mind that they get the full complement of carry on luggage. (namely suitcase + backpack + airport purchases). I assume that you've thought that through, and am just pointing it out on the off chance that you haven't, because it's a lot of extra stuff you could bring.
In my experience, it was an ungodly hassle to move everything I had, but I just made sure to avoid creating a traffic jam when getting on and (especially) off the plane.