United seem to be under the impression that this is not possible without an empty seat between us, because they believe that airplanes are constructed with "one extra" oxygen mask per sections of seats.

Isn't that a bit presumptuous to state it that way? If there is only one extra O2 mask in each row, there is only one extra O2 mask in each row. End of story. Two adults with two lap babies can't sit there.

I worked for two airlines and I never remember more than one extra O2 mask in each row except for one aircraft which had 5 across in the middle. There were two there.

Sit across the aisle from one another.

Email the company and ask this question. Don't call since the revs agents usually don't have this information and can basically say anything over the phone. An email can be printed up and shown to an agent if the seating is questioned.

Please don't sit on the top deck with two lap babies! The lav situation is better on the main deck and you can take walks with them more easily through economy if they get antsy, if it's a long flight.