one of my mother's more unhinged rant topics was women intentionally keeping children away from their fathers as revenge for him breaking up with her and that if they don't have the maturity to get married and stay married then they shouldn't have children etc etc. She also talked mad shit about people who take government assistance to care for their children when my disabled sister has always been on as many benefits as my mother could get approved (she had good reasons though, unlike those lazy "other" people... 🤔)
ime I have seen mothers use their child coercively but it's not usually by keeping them from the father, at least not successfully. It turns out family court actually favors fathers if they bother to pursue custody, which few do without a strong reason, either good or bad. It's usually been women using the children to coerce family, friends, or a new partner into staying by getting them to bond with the child then being able to actually remove the child from them since they have no legal rights to the child. And I think the only reason I haven't seen fathers do it more is because, as stated previously, many don't pursue custody due to either internal or external expectations that childcare is the mother's job.