Is it permissible to remain in the police academy despite missing some prayers and enduring repeated verbal abuse, given the family's objection to resignation and the unavailability of a vocational alternative?

If studying at the college leads to missing prayers on time, and to the presence of cursing and foul language, then it is not permissible to continue in it, and it must be left, because safety in religion is unparalleled. There is no obedience to a creature in disobedience to the Creator. As for sustenance, it is in the hand of Allah, and "whoever fears Allah - He will make for him a way out and will provide for him from where he does not expect." A person may be deprived of sustenance due to a sin he commits. It is advisable to look for another institution for study and to advise those in charge of the college administration to rectify the situation.