「家族関係に悩む」は
ーto be troubled by family relationships
ーto have trouble with one's family
のように表現できます。
例:
I have a friend who is having trouble with his family.
「家族関係に悩む友達がいる」
I have a friend who was abused by his family (in the past).
「(過去に)家族に虐待された友達がいる」
to be abused by ... で「…に虐待される」
ご参考まで!