The way I read the OP's original post is that the horses are normally out, but the paddock is also the riding area, so she needs to put the other mare up while she rides for safety reasons. I also believe that this is not the OP's property, and that her horse and this big mare are both boarders, which limits her options somewhat.
in general, I agree with the comments about stalling more than 12 hours per day being unhealthy and anti-instinctual for the horse, and that stalls are a human contrivance and convenience, however, I don't think that really applies in this situation.
And I agree with the posters that said horses need to learn to accept being confined; it's just basic submission/obedience. My horses are out 24/7 with run ins, but if I need to put them up for the vet or farrier or any other reason, I expect them to settle in and accept it after some initial pacing and fussing. Just as I expect them to stand tied, or stand on the trailer.
The Belgian mare sounds VERY herd bound and buddy sour, that, combined with being the alpha mare, is quite a handful.
If you don't have the available space to do as Spotted suggested (very good suggestion, btw) I honestly think in this case hot wiring her stall may be the only way to proceed. I have seen it done to deter cribbing, it's not pretty but it does work. I think the inherent danger in this situation warrants an immediate and serious remedy.
I am trying to imagine hacking around a paddock when this beast breaks out of the stall and tries to herd the horse I'm riding - Yikes!