parental controls for 14yr old iphone.

Is there a possible way to keep my teen out of inappropriate websites without setting the phone on a "kiddie lock"? It doesn't seem like I am able to let them browse the internet for things without getting on specific adult websites but not limit them to just children websites. I had type in the NEVER allow spot some websites but they were still accessible. Also, It doesn't seem like I am able to clear the search history for my teens phone on my end and I would like to do that. Is there a way to get that done? Is there a way to get a search history for safari from my end for their devices?