6'10" in economy class with a 1.5 year old lap-child sounds far worse than 5'4" in economy class with a 1.5 year old lap-child.

Many a person in my family have traveled from the US to some far reaches of Asia and South America in economy class with or as a lap-child infant where there was only one adult person in the travel party. And it has been far smoother than it has been in my family where there has been only one adult traveling with two or three seated young children in business or first class on such trips.

The key thing generally is that of being able to maximize the proportion of total flight time that is sleep time for the lap-child, to let the child find some mobility time (preferably on the ground), and to entertain and feed the child to the child's content on the flight. A well-rested caretaker helps, so hopefully there will be some breaks (at least on the ground) in this regard.

He did say he's looking into a third seat, one in economy class. That should thrill her indeed, more so if a car seat is allowed on board for use (which is far more likely if having a confirmed seat for the child). No need to feel sorry for either member of a couple when talking of couples arriving at outcomes which they both consider acceptable.