My car did that and it was a bad exhaust. I had to replace it because it eventually broke a bracket. When that happened it made a horrible vibration sound in first to second gear. Maybe they can look at it and just see if it is loose.

At 16 the issue is more that it is illegal to have sexual relations with her. I would definitely hold off on moving her in.

You have to register with your state. Ex. Texas Workforce Commission. Go online but in our state you apply every two weeks and have to apply to at least 3 companies a week. It takes a few weeks to get it going so don't delay.