I don't think status has anything to do with it, as I'm not aware of any PE fares on AFKL that don't have free seat selection (this isn't BA)
If I had to guess, you're hitting some constraint on placing your 2yo (e.g. it may require a window/middle seat next to an adult on the reservation). How full are the cabins on your flights?
It's also not impossible that the bassinet seats are blocked from selection until gate assignment (I believe there are some airlines that do that in order to minimize needing to move people out of bulkhead seats).