I don't think there are many options in this scenario if you don't want these kids running around your house like this and if mom is not getting the hint from you requesting what you want in front of her.
One solution could be to step outside with this family to have your post-lesson conversations -- act as though you are walking them out -- this could be a very quick and painless fix.
You could also try talking with the kids, one-on-one, before mom comes to pick them up (though, this will have perhaps varied impact and I am assuming you have already done this to *some* extent). "You know, Sally, when mom comes to pick you up I need to be able to talk with her about your lesson. It's very distracting for me when you are running around the house like you do. And, just because mom is here does not mean that my rules don't matter anymore --
I know that
you know what I expect from you while you are here, because you have already shown me that you can do as I ask of you. I appreciate it when you listen to me and respect my requests of you." -- some kids will respond to that, some won't. Which one of them is the instigator ? Try to get him/her on your "side" first.
But, if these are not an option/not working you will need to talk with mom.
Kids are interesting people

. No matter what, they will fall back on the rules of the person's whom they think is in charge of a situation. Obviously this behavior is what they are used to when mom is around. It sounds like when they are alone with you, they behave differently; that's because they don't feel like there is anybody else there to give them permission to do otherwise -- they *do* know what your expectations are. It is *very* common for kids to be different people with somebody like you vs how they are with mom or dad.
You are going to need to talk with mom one-on-one because she is the one whom needs to know, exactly, what it is that you need from this situation, and what you need from her in order to have it come about -- directness, coupled with tactfulness

.
Honestly, I think sometimes parents are so overwhelmed with their lives and the job of parenting (which is a HUGE job), that they get to a point where they "don't notice" things like this -- this situation becomes a "battle" they choose not to pick. Mom needs to realize that this "battle" is indeed important, and you need to help her realize this. She also may just have different expectations of her kids' behavior than you do (in other words, perhaps it's not just a "battle" that she is choosing not to pick, but a whole different philosophy about behavior altogether).
If it doesn't seem worth it to you to have this conversation with mom, then you are going to need to grin and bear it unless you find another solution.
You can also just plain bribe them without involving mom at all

.