Sons Girlfriend (Long)

Our 16 yr old son has had a girlfriend (she's 16) since August. It's not been anything serious, and I'm glad. But.... She wants him to do things that could potentially get him in trouble. She's 16, and the rules are (according to her Father, and us) is that they aren't to go anywhere alone, and if they do anything together it has to be a school function, or with friends at public places, and he has to know about it, and approve it first by speaking to my Husband on the phone before any plans are finalized. She's already lied to her Dad, and used her Mom against him when asking for permission to do things, and it's been a mess.... Our son isn't the most mature for his age. He has his drivers license, and has been looking for a job, and does good in school, but it can be a struggle sometimes. We limit what he does because he's not the best at making decisions, so we're trying to protect him from himself.... And by decisions I mean like thinking things through, before doing them. Thankfully he knows to come to us first.
We do trust our son, but not her, we don't really know her. I read a text on his phone that she said to just tell us that she doesn't have to approve anything with her Dad anymore, and our son told her no, that's not a good idea. Then she posts pot pictures on her FB page about how good it looks, etc (we monitor our sons, and he knows it). We spoke to our son last night about it all, and he's just so hooked on this girl. She still does sleepovers, no drivers license, and no goals that we know of. According to our son she doesn't have the best grades, and to me just seems very immature for her age.
I've offered to have her over for dinner, or to hang out and watch movies, or go out with all of us, but it's always a no from her. She told our son that she's scared of me, but I'm not sure why. I'm nice to her when I see her, I'm guessing it's because we're very strict parents.
Don't get me wrong, our son is able to have fun. He has a dirt bike, his own jeep, he takes them to offroad parks with us. He's learned to take care of both, doing oil changes etc. He helped rebuild the engine in his jeep with his Dad. He stays very busy here at home. We are very family oriented, we talk a lot, and have a lot of fun together. We're also a hard working family, and our son knows what's expected of him.
So, my question is this.... Are we wrong to tell him to put a stop to the relationship (which here lately is only at school)? We don't plan on telling him he has to, but is making the suggestion wrong? I have told him that he should focus on school, and finding a job, but he just looks at me like a sad puppy... (Yes I know hormones are in play here, I'm not naive..)
I just don't feel like she's good for him. She's out to just have fun, and party by the looks of it, and we want him to be with someone that has goals, etc...
What would you do? Thanks!

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