While this family situation sounds distressing, it would be ill advised to kick a 15 year old out. Parents generally have a legal obligation to provide for the care and support of their minor children (including housing) although it does get complicated when a child runs away. Those obligations usually end when a child turns 18 or when a court gives a minor legal emancipation or when parental rights are terminated. You don't describe what involvement the biological father might have or if the father holding custody might be an option. Sitting down with a family mediator and/or an experienced family counselor who has dealt with similar situations might be a good option if everyone is willing to do so. If the stepdaughter is unwilling, a good counselor may still help you and your wife. You may also want to enlist the help of the school guidance counselor or social worker.
There is no legal obligation to give gifts to a stepchild and a counselor might help map out certain ground rules / boundaries / natural consequences associated with living in your home. This post is not legal advice and but I do hope it helps offer some general suggestions.
