Irrespective of whether or not it is a Mitzwah to give a Get even if man wishes marriage to remain effective and get back together, Nothing changes the Father’s obligation of Talmud Toroh and veHigadto leVincho on Seder nite, towards his children. To this end, if any mother ever withholds parenting time for the father, she is definitely causing Toroh obligations on the father to be non-observed.
So much so, that in Jewish Law, when a Boy reaches age 6, the Father gets custody of his son, to teach his son, Toroh. Until such time as a Beth Din follows this Halocho, why should they be forcing Father to give Het to Mother, but ignoring Toroh laws of teaching Toro to his son?
In many cases this is the only leverage the father has, to get his parenting time, to teach his children Toroh, so he should absolutely utilize this leverage of withholding Get to counteract the Limud Toroh to his son that the mother is withholding from the father.