It should be this: "His mother thinks THE WORLD of him and has done everything she can to come between us and try to split us up." It means that my boyfriend's mother loves him so much that she has tried everything possible to end my relationship with him.

If you reword this sentence, it may make more sense. His mother thinks the world of him (or has a very high opinion of him) so (as a consequence) she has done everything possible to come between us (or separate us) and try to split us up (or break our relationship).

I think the sentence should be... "His mother thinks THE WORLD of him and has done everything..." In English, if you say "I think the world of him" you are saying you think he is wonderful and he can't do anything wrong. It is a very exaggerated admiration for someone. Perhaps the mother thinks that no woman can be good enough for her amazing son. He's just so perfect !!! So she tries to break up his relationships so she doesn't have to share him with anyone.

یعنی پسرش براش خیلی عزیزه به همین خاطر فکر میکنه دختری که تو زندگی کنونی پسرشه برای پسرش مناسب نیست و در تلاش که ما را از هم جدا کنه