Here's a simple explanation that fits all the information given:
Parents are religious. Their daughter married a man of the same religion but later ceased to be religious. Their son-in-law abandoned his wife and son, but stayed within in the church or on the derech or whatever. LW's parents refused to support their daughter unless she repented and returned to the religion, which she thought of as refusing to support her. She doesn't phrase it this way because she doesn't want to get into religious arguments.