I don't have any precise house rules like those discussed above -- indeed, I'm perfectly happy to shop players and initiate trades. Instead I find it better to use some over-arching principles:
1) Never make a trade that I don't think is a good trade for the other GM. Often I will make trades that my own manager isn't sure of: my analytical skills are better than the AI's, and I resist the temptation to take extra advantage.
2) Actively intervene to help AI teams improve themselves: if a good team is benching one of its most effective players, or allowing a giant hole in its lineup, or refusing to spend its large surplus of money, I'll jump into that team's shoes and see if I can do something clever (a good trade, a signing) to fix its problems.
3) Similarly, if I see a good player on waivers, I will either step into the shoes of the waiving team and Shop that player -- allowing it to trade instead of lose the player -- or, if for some reason I find the waiver decision believable, I'll nonetheless pass up the chance to claim the player for myself.
4) Once my team is a champion with a strong farm system and/or lots of money, I leave it and hire myself on to a much weaker team.
5) Also, since i run two teams at a time - one per sub-league - I do not allow them to trade with each other, and as much as possible I don't let the knowledge from one team's scouts affect the other team's draft decisions. (This has meant, for the last two drafts, having one of my teams make high-ranking choices that my other team would have told them were dumb, just because Nazca's two best scouts had simultaneous delusions. So it goes.)
*****
In my current league, my original teams included Guopore, which I left after three years, two straight pennants, and a world championship - they now have won their division six straight years, because of the strong position I left them in. They also included Hudiksvall, who I left after three pennants and two world championships in five years, and have won two more division titles and one more world series in the two years since. My post-Guopore team, Trujillo, went immediately from 73 wins to 99, won two straight pennants and a world title with me, and I left it after just two years; it won the next division title as well, and only lost last year when I took their division rival Nazca from 67 wins to 100.
In other words, my biggest house rule is that I make my own opponents good. Then I beat them anyway.