Timing wise, was he suggesting you would be applying to Princeton SCEA if the slot becomes available or would you have to wait until December and apply RD? Waiting until RD seems risky because you may be giving up any SCEA bump there is for legacies. And I expect there is one but don’t know for sure.
If you don’t take the Brown offer, you might tell the coach family pressure is involved in applying to Princeton SCEA (as some others have suggested) and you have to try. Then ask if a fully supported slot might be available in RD should Princeton not work out. If not, ask if this coach offers ‘soft’ support in RD or would there be nothing in the way of support but hopefully a spot on the team if you get in on your own.
Separately, is your app and all essays for both schools ready to go? I also strongly encourage you to get some EA apps in (following any application rules that Princeton SCEA has if the ends up being your choice.) Good luck!