I had never even tried to bend the upper or lower jaw pieces of the Therabite but after reading your post, I did. Surprisingly, my upper one also flexed easily just as you described and just as much. I'm not an engineer but this suggests to me that the problem is not with the device. Since you have configured your therabite correctly, the only variable in the equation appears to be your mother's "biting". The force of a biting jaw is very powerful and my therapist did stress that I had to consciously refrain from biting down on the mouthpieces. The teeth just go along for the ride, they don't press back.
This must be very frustrating to you and I wish I could solve it, but Trismus is a big issue that keeps coming back (I've been struggling with it for almost three years). I know there are similar devices to the Therabite such as the Dynasplint but their web photos looked very very uncomfortable and weird to me.
Finally, it could also simply be that the damage to your mother's jaw muscles and nerves is simply too great to be remediated by any device. I sadly know this in the context of swallowing where every exercise or device (including the vaunted VitalStim electrical therapy) has not worked for me.
You are a very good son and caregiver
Charm