Hypervigilance is a well known trait of Post Traumatic Stress, which I have, and if your daughter's experience of her mom's death was traumatic, she may be dealing with some symptoms of that, though of course, only someone like the therapist would have enough information and be qualified to evaluate things like that. However, I wanted to mention it just to give you some context into what I know of hypervigilance.
My experience of hypervigilance is that I am often on high alert for danger. I do not relax well. I pay close, almost unconscious attention to everyone and thing around me, as if something bad might always be about to happen, even when that is extremely unlikely. I may overreact to a small conflict or demand in a defensive, startled, or upset way.
So, when you talk about your daughter scanning her environment and staying near an exit, yes, that sounds like hypervigilance, perhaps due to a mistrust of the therapy process or the therapist, or just a response to her life right now. She must be having a terrible time losing her mother: there is very little tragedy in the world that compares with a loss like that.
Hypervigilance can be a problem in therapy if the client and therapist do not build enough trust for the client to be open and honest about their feelings and issues. However, hypervigilance, or, more really, a lack of trust is super common in therapy, and the therapist should be well experienced in working through it.
I am sorry you are feeling hopeless. I am a mother and have never felt any worse feeling than seeing my daughter has a problem and not being sure how to best fix it.
My own therapist tells me sometimes to just be accepting. I try to be gentle and empathetic with my daughter, and patient, I think those always help.
How long has she been in therapy? These things can definitely take time!
P.S. As far as hypervigilance being "serious" well, it's a stress response that can be worked through, but some folks do take medications for anxiety and such to lessen it. I am definitely wary of medication like you, maybe her therapist could explain to you exactly how much good she thinks it would do, which symptoms she things need addressing and why. I haven't heard of hypervigilance by itself being treated much with medication, but... that's just me.