I think the children in WT won’t be a problem under normal circumstances however the problem here is an adult In F swapping for a child and therefore paying the child F fare which is heavily reduced over the adult. Crew will be aware of this and it won’t be allowed. Your wife can of course swap with one of your other children to remain with you in WT

if crew push it could be classed as attempted deception and deliberately trying to save as much as possible eg booking child into F as opposed to the young adults. Could be seen as premeditated to try and get 2 adults into F.