Without the specific carrier and exact route, nobody here can provide an exact answer.

But, the general answer is that each passenger will need a seat and will need to be able to occupy that seat during taxi, departure, landing, and in turbulence. This will mean that the child and one of you will need to be ticketed in either J or Y as the case may be and that the other may be ticketed anywhere.

Some carriers might permit a brief swap of parents when meal service is not being conducted and with the permission of crew, and others will not do this under any circumstances.