if you see different behavior then the vehicles in sandbox map then the first thing comes to my mind is the tire model, avoid using TireSimple if you are not making slow moving vehicles. also too much slip can cause instability for rwd vehicle so you can try a couple of things like increasing wheel mass, antirollbars etc. There are only 2 curves used in the StandardInput component, one is for speed vs steer angle and the other is for speed vs steering speed. If you need more complicated stuff you can modify the source or build your own input system through BP.
As you said you can modify the input component or you can scale the braking torque depending on a curve from BP.