A birthday present for you is an acceptable secret, so is working on himself through therapy or something like that...everything else is bad news.
I did detective work on my ex for years, and all it did was make me miserable. I was also violating his personal boundaries by doing so, and he violated mine. Re-read that thread on boundaries if that might help you.
As long as he finds anything sneaky acceptable, you won't see eye to eye. You can hire a PI, you can put a keylogger on computers, and that will bring you the truth of what is going on, but it sure won't fix the two of you. Sometimes detective work can bring to light what is going on, but then you have to be ready to act on what you find out.
Changing his mind about his behaviors is the long-shot, even if you throw it in his face.