When the bracing happens you keep your hands the same and then use more leg (or even a tap with the whip) to correct the bracing. If he tries to spurt forth or otherwise convince you to change your plan, don’t.
Your trainer is having this same conversation, just very quickly.
My horse is a dedicated specialist in this particular evasion and Vera Kessels taught us a great exercise: ride a 20m circle btw B and E. When crossing center line, do a 10m circle to the outside of the circle (so changing direction). When touching B or E do a 10m circle to the inside of the circle. The constant circling and bend/direction changes means you can’t get locked into one oppositional discussion; everything keeps flowing and if you need to do a quick wallop in the ribs to get him OUT IN FRONT of your leg, the circles will keep him from spurting out too far forwards, and then in two strides you’ll be in a new bend again and moving on so nobody gets mired in a tug of war. The horse will figure out pretty quick that there’s always a turn coming up so he’ll dtart carrying himself accordingly.