Install a keylogger would not work he is a computer programmer and would find it on his computer.
You don't know that. The POINT of keyloggers is that they don't reveal themselves and are hidden. Unless he's regularly reprogramming his own computer, and he has no reason to be doing that, he'll never think to look.
And if he does, SO WHAT? You should be MAD AS HELL at him for putting you through this, especially with what you're dealing with. How dare he? SHOW him that anger. Make him AFRAID TO LOSE YOU. You have every right to search for proof at this point and if he dares to get mad at you, then you know he's a POS and doesn't deserve you. Consider it a sh*t test, and you need to know the answer one way or the other.