"Unassertive - sometimes my staff (they are all gone by now) used to talk back to me/not do stuff etc.; I either let it slide, or I try to tell them nicely that "this is not the way to do things etc." and they do not listen, but my business partner gives them a look and they listen to him."
OK, I see this in a new light now. Theoretically these people are subject to your authority, but they've gotten the idea you're too nice or weakwilled or something to do anything if they slouch around instead of toeing the mark. And you, being INTP, are reluctant to drop the hammer on them in an authoritative way.
But you'd have no trouble being a tough guy if a principle was at stake or if, the best condition of all, all suffered because people were not pulling their weight.
So, at the risk of sounding like a despicable middle manager who actually read the book, here's what you do:
1. Continue to nicely say "This is not how we do things" and make sure you present "the way we actually do things". You can even present "why we do it this way," since sometimes that actually helps.
2. Quietly chart progress and change or lack thereof. After three days nicely say "I see you are still doing things in ways you were told were not the way we want it done. Please don't make me have to bring this up again."
3. Chart progress and change or lack thereof. If we are still on "lack thereof," talk to your partner about what you have done and what you have observed, and get his backing for step three, which is
4. Nicely call the person into your office, with your partner present, and tell the person, nicely, that they have ignored two calls to action and you are not required to put up with their lack of respect for the way the firm operates. Hand them their last check and tell them arrangements will be made for them to come back when no one is around to collect their personal stuff, if any. Then tell them you wish them luck in finding a job where they can do things their way and escort them to the door.
I had to fire very few people over a 40-year career, but I always made it a point to do it in the same calm way I did business on the newsroom floor, an amiable guy showing folks how it should be done and just as amiably telling them to hit the road if they -- key point -- didn't follow the program. Had nothing to do with me. It had to do with the program. I believe the ability to not change style during the firing kind of enhanced, long-term, the idea that "he doesn't sound threatening, but he really means it, so toe the mark which, after all, isn't so very hard to do."
Understand, my field had a lot of flexibility for performance and a lot of room for people to follow their inclinations, but at the end of it all there were indeed standards for producing and, especially, for meeting deadlines and whatnot. Your mileage may vary.
This process, this arrangement of impersonal measurements for job performance, seems to suit the INTP temperament. It gets your ego out of the way, which I suspect is one of the problems all of us have when forced to interact with others. That chameleon character we're supposed to have, so some extent, as INTPs, really does us no favors when we're in a supervisory or authority position, ya know? So you have to make sure you put the whole process in some other place.
One more piece of gratuitous advice: Those people aren't your friends. INTPs sometimes have a dangerously self-deceptive tendency to equate familiarity over time with friendship. You may work with someone for five years; you may be a lot more comfortable with them than with a stranger; that person is still not your friend, especially if you are the supervisor and especially if you have no outside-of-work contact. It is professionally dangerous to YOU to think they are your friends. Treat them with courtesy, but not as you would treat a friend. Read this about 20 times until it sinks in. It's a really important factor in the "professional INTP" survival bag.
