Employer A is not only paying you to fly his airplane he is paying for you to be available to fly anytime.
I can understand your employer's heartache with it. They pay for your training, your health insurance, workman's comp and all your benefits. You can at least give them what they pay for.
I am sure you took the job knowing you were to be available to them at all times.
Do you have hard days off? Will you reimburse your present employer for pro rata training?
You boss is just being prudent and I amsure this is not the first time in his life an employee has tried to moonlight. He probably doesn't allow his legal council or accountants do it either.
Be careful, when it comes time for a raise he will be less inclined to grant one knowing you are making money on the side.
Boundaries need to be set. For hard days off and for outside flying.
The last thing he wants is his pilots out of town when he needs to get somewhere.
Owners keep an airplane and full time crew for the perceived value of having it available anytime.
It aircraft B needs a crew, have them hire a full time pilot. Work out a mutual pilot sharing arrangement to cover each other's trips when you are sick or need a day off etc. Both sides win.
Good luck, let us know how it goes.