Hi, you can teach any horse to do anything provided it is willing, there is absolutely no reason why your mare wouldnt be able to do this, before you start she will need to be schooled to a reasonable level and be able to do a balanced canter. Start off by cantering round the school and go to change the rein across the diagonal, just before you reach the middle ask for trot for a few strides and them puck up canter on the other leg and continue aroung the corner, gradually decrease the amount of strides of trot in the middle
I like to use a slightly different method to teach lead changes rather than just gallop in figure eights and pull on the other rein. Does your horse have decent lateral work? I use leg yield because it gives all the right signals, and can be started at trot. Start out trotting on the left rein. When you reach the end of the ring, do a half circle (fairly small one so you don't have too far to go) and leg yield back to the wall (using right leg). As soon as you reach the wall, make sure your horse is bent to the right, switch your legs (now apply more left leg) and ask your horse to canter off on the right lead. Keep your horse straight through the leg yield and transition. When the horse understands this exercise in both directions, try it at canter. Left lead canter, half circle, leg yield, (left lead, right leg on) when you reach the wall, change your bend, switch your legs, and ride forward. If the horse does not get the lead, try more work from the trot, or put a pole on the straight wall. This way if he doesnt switch when you ask, there's a pole to help him a couple strides later. This method will allow your horse to stay straight, and he will change leads when you change your bend and your legs. Exactly what you want.