Like the last guy said your parents are trying to help. It took my family a few years and several talking to's to get them to back off. More than likely they see this as a roadblock more than an open door. You have to realize that although all parents want their children to be happy they do not raise them thinking that they will be landscapers. I had similar problems where they would suggest I lower prices and offer discounts, because in their mind the answer was volume and multiple crews early on even though that did not match my business model.
There were several times that promises were made for me that I was expected to deliver on, but which I wanted no part of. For example, my father's good friend was using the only real strong competition I had at the time. Large house, $100 mow, etc. One day the wife said something to the crew that set them off. They left mid mow and did not return. Calls were placed and a promise was made that we would cut it for $50, 10 days after the incident, so half being a 2 week growth. The catch was that they had worked out the issue with their original guy and were going to return the following week. So for me it would have been a one time service, overgrown, non contract, and under priced. All of these went against policies I had. In the end I did not do it and there was some feelings about it, but I had to look out for myself. I also had several family referrals that turned out bad because they were expecting the 12 year old lawn boy price and not a competitive landscape contractor price.
You are young and still in the house, being a minor you can not even run your business legally. My suggestion, is that you separate family and business, but stay in the house as long as you feel it is right and financially smart. I'm not saying stay till you are in your mid 30's. All my similar problems happened when I was in my mid to late 20's, owned my own house, and was clearly capable of taking care of myself. My point is that moving out will not solve anything. My family leaves my business alone now, but they have moved on to other things like back seat parenting my son, etc. I guess parents will always be parents, and no matter how old you are you will always be their baby and they will always think they know better than you.