agreed with ebeth - your mom panics...why? Your past history and perhaps knowing your boyfriend is also a former addict. Is this completely fair? No. Is there a reason? Yes.
You need to put your children first - bottom line. Your mom is trying to do this. I think hearing you use the words "panic" leads me to believe she loves you lots and wants to do this for you, but her thoughts of the children come first - and this is why she "panics." She wants to say yes - but she wants to protect the children. Of course - this is a complete feeling/guess from my side but I can feel the conflict she is having.
Agreeing with ebeth - your boyfriend is a grown adult so your mom cannot stop him from coming as long as he has his own accommodations which I would recommend any way.
Have you asked her? I mean ask her the situation we proposed? That they come meet him, but leave the children out of it. So your mom/dad/other trusted family adult could get to know him. Seeing your mom is guardian is completely makes sense that she does not allow another adult to become part of these kids lives until she gets to know them and feels the children would benefit from such a relationship. Your mom is their protector and should NOT allow any adult to form a relationship with them without knowing them first and feeling comfortable this is good for the children.
Maybe if you approach it that way your mom won't panic. She will see you also want what is best for them. Take it slow. You probably had to do that to be successful in your recovery - this is just one more step -- and it impacts the lives of children. Take it slow and if what you say is true - this guy is that great and you are going to be together for the rest of your lives...waiting a little longer and working with everyone so it is best for the children will show what a true caring mother you are.