I think you already know what you need to do. You tell the other parents that you will no longer be allowing your daughter to come to their home since they are allowing underage socializing between your daughter a boy. That you have said she is not to be around him unless you are supervising their actions.
These parents may have been told anything and they may not even know she's not supposed to be doing this.
You also need to contact his parents and let them know she's restricted and why. They may not know where their kiddo has been and what lies he's been telling them too.
Also, you are the parent and yes, you should not allow her to do anything that you don't take her to and stay there and then bring her home.
When she asks why or yells at you that you're being mean simply remind her that you did trust her. That her own choices to sneak around and see him have made it impossible for you to trust her right now and once trust is broken it takes a long time to repair it.
Tell her she has until Christmas to prove herself to you and that she is trustworthy and will tell you the truth and do obey this rule about the boyfriend.
If you don't it is likely she'll end up pregnant. Kids without proper supervision don't make great choices.
My friend that grew up with parents that didn't think the kids needed supervision ended up with 4 kids by the time she was 20. Her parents had a wonderful basement. Tons of kids from high school hung out at their house every evening. They had low lights and bar lights over the pool table. It had a juke box and big speakers, a totally cool place for the teens to hang out.
Problem was over half of her senior class had at least one child before they graduated, if they even finished high school. Guess how many of them got pregnant in her basement...almost every one if them because no adults were around helping to make sure these kids weren't faced with adult choices before they should have been.
Your daughter has shown you that she isn't mature enough or smart enough or old enough to date. I think you are very right that she should not be allowed to see him alone. She's making bad choices and lying about it.