Be prepared that they may be sitting alone, especially the 6 yo. The FA's will go to great lengths to try to get an accompanying adult seated next to a 4 yo, but the base age for flying unaccompanied is 5, so they won't go so far for a 6 yo. Make sure that they have quiet entertainment, a water bottle and snacks in a bag that each child is carrying.
If the 4 yo is still under 40 lbs., you might want to consider taking a 5-pt. carseat for that child -- being in it will guarantee that he/she is in a window seat with an adult along side, because that is an FAA regulation for carseat use. If you plan to do this, call the airline and tell them that she will be traveling in a carseat; they may be able to give you an assignment for those two seats under those circumstances.
Get to the airport as early as possible, and tell both the ticket agent and the gate agent about the problem, so that *if* they can get you contiguous seats, they will. If you cannot get contiguous assignments from the ticket agent, take whatever they can give you and try again at the gate -- you have to have boarding passes to go through TSA security. (And I disagree that 3 hours is too early in this situation -- seats that are held for assignment at the airport go first-come, so the odds get worse as you get closer to departure time. I wouldn't go further than 4 hours out, though.)
If there is just nothing left but middle seats, keep an eye out for situations where there are open middles stacked one behind another. While not ideal, of course, that at least puts the adult in arm's reach of the child, and in a position to talk when necessary. In that situation, it is best to seat the adult behind the child, because it is easier for the smaller child to turn around in a coach seat, and easier for the adult to keep an eye on how the child is behaving.
I haven't flown UA with a child since they implemented E+, but a tactic that has worked for me in the past (on other airlines with somewhat similar policies) in a situation where I needed two seats but only had one, is to offer to pay to upgrade a single traveler other than myself. The GA can look at passenger status and seat assignments and may be able to find someone suitable who will be happy to take a "free" upgrade and open up that needed coach seat pair. (It's not that I have an issue with paying to upgrade myself and a child, but sometimes the only seats left in either category are singles, which means that you've got to find a party of one to be able to make the switch.)
Also, just as a general rule when trying to negotiate for seats: always suggest taking the least desirable of the available seats for yourself when trying to work a trade for a contiguous pair. You are far more likely to find someone willing to go toward the front of the plane than the rear, or into an aisle seat than a middle. (I know that this is obvious to those who fly fairly often, but people who almost never fly are sometimes unaware that there is more value placed on certain locations and positions than others, so this is just an open FYI.)