I have been a studio photographer in multiple different cities, and the type of mother you describe exists. We used to shoot a lot of sets every day, and I have run into quite a few of the bossy-type moms. Moms actually ruin a lot of photo sessions by looking at the kids to be the smile-police, when the mother should be looking ahead, at the camera, like the rest of the family. Moms can ruin sets by directing the other family members. As has already been said, you must be the alpha. You establish that from the very start of the session. Tirediron's comment is one way to handle a bossy mom (in thousands of sessions, I never once met a "bossy dad"); tell her, "We can try some shots your way," and then you can do that, but then you say, "Your way isn't working, let's do it my way." That immediately undercuts her judgement.standing in front of the others. The other way is to say, flat out, "I'm in charge, let's shoot this this way: ___ __ ___ ____ __ ___,with ___ _ ___ __ ___ ____," However, making a bold, alpha who-is-in-charge type of statement takes some gumption, and many people will not do it, either out of timidity or respect or for some other reason.
Nychimages, your profile photo makes me think you are young, possibly female; if you are young, either male or female, it could be that the mother feels like she's hired somebody who is nothing more than a so-called "hired gun", somebody who will listen to her, "the boss", and who will shoot to specification, exactly as-commanded. Perhaps there was a miscommunication before the session, or perhaps the mother had some very specific ideas about what she wanted photographed, and exactly how she wanted it done.
Anyway...get used to this "bossy mom" type of behavior unless you realize that, to discourage and minimize it, you must be the alpha; you must be in-charge, and in-command during a studio session. This has to be made clear in a pre-shoot consultation. You simply must make it clear "how" the session will be done. There can be room for pre-planned poses and pre-planned groups, and there can be room for free-form posing and loose poses and spontaneous ideas, but ALL of that needs to be talked about, BEFORE you start the session. If, during a session, there is some problem, you need to solve the problem by your own command. If somebody is acting up, you need to use your voice to tell the person(s) to behave better, or to leave the area if they are doing a peanut gallery behavior (like trying to play smile-police).