Settle it before the conversation, not during it

A disagreement discovered live, in front of the child, turns a decision about their future into a contest between the adults. They stop thinking about the choice and start managing the room — and whichever way it lands, somebody has been defeated in front of them.

So have the argument first, privately, and take as long over it as it needs. Arrive at the conversation either with an agreed position or with an agreed way of presenting two positions. Both of those are fine. What is not fine is finding out at the table.