Regarding trail braking ... the new engine behaves more like a real car. If you are pushing, it means that you have all the weight transitioned to the front outside corner. That tire can only provide so much grip before it lets go. Once it lets go, your car will continue in the direction of travel of the vector you are on.
How to solve this ... you can't be in your threshold braking zone to do this. Go deeper into the corner, slow the car down more and then roll into the corner and trail the brakes decreasingly down to the apex. This does a couple things. First, you're asking a whole lot less of that outside front tire. Second, you settle the car down more and the other three tires carry more of the braking and cornering load.
In a nutshell, you're going too fast if it's pushing.
HTH,
Michael