Surely the father (in your scenario) would have also had the same recourse to legal representation if he was not on a high wage/any wage as the mother did.
I know of two cases in the last few weeks where the estranged father has snatched the children from the mother (during access visits) and refused to give them back, in both cases the father was having good access to the children and did it out of spite. In one case the child concerned is (supposedly) being returned on friday, the other case is unresolved because the mother (my daughter) has no access to legal aid or any funding to take the case to court.
I know in the past some mothers have abused the system but in both cases detailed above there was no need whatsoever for the fathers to snatch the kids. My grandsons are being used for benefit claims by their dad because he can't be bothered working, whilst my daughter is working her @rse off to try and save up enough for legal fees to get her sons back.