Is it permissible for me to trim and neaten my beard due to pressure from my parents and their fear for me regarding the difficulty of marriage and security issues, so as to avoid disobeying them?

Trimming the beard is Haram according to the majority of scholars. As for shortening it or grooming it, there is a difference of opinion. If parental pressure to reduce the beard intensifies and leads to major problems that could result in disobedience (uquq), then there is no sin in complying with their command to shorten it, especially if their fear for the questioner is due to security concerns.