Originally Posted by Erasmus

Crew would definitely frown--as likely other passengers in J when they see people moving back and forth. In general, one must stay in your ticketed cabin. Short visits are occasionally tolerated (depends on the airline), but frequent swapping will certainly raise an eye. If you booked tickets this way I'd expect to have to manage both children alone in PE while your wife remained in J for the duration. (And you said "tickets", not seats. Everyone will need a ticket, but the infant does doesn't get a seat unless you pay for it.)

Originally Posted by GUWonder

That’s how I see it too, except I would add that on regular paid tickets the infant doesn't get a seat unless the OP pays for it or gets lucky with having an unoccupied seat adjacent to one of the travelers in PE.

I would also add that some airlines may be more uptight about some people moving between cabins than other airlines are — even with regard to “self-downgrading” temporarily.