All looks healthy there! Plants and grass don't mix well. What are you wanting to do here? Maybe I don't see the problem you so! I use a spray called GRASS GETTER to kill the grass that gets into my flowers and shrubs. Kills the grasses but leaves the plant unharmed. Please point out to me you issues in the pics.
Most people would kill for a yard like that however you need to tigthen your beds. If you can try to find steel edging 3", do not put down that plastic garbage. If not then go with a brick edging. Don't listen to some "garden expert" that knows how to dig a hole and nothing else.