@blatham,
To what degree, legally speaking CAN he bully them, do you think? Don't they pretty much all despise him, but didn't have the guts to say so?
Also, in your system, how much non legal power does he have over them? eg how much will they feel they need to appear to support him?
Our Prime Ministers have a lot of bully power, for instance, politically but not legally speaking.....UNTIL they begin to look as though they are not going to help their back and front benchers to stay in their seats at the next election. The members can get rid of a sitting PM if they have the numbers. They have done so numerous times.
Conversely, our Prime Ministers can have very little bully power if they are beholden for their position to a particular faction. Both Gillard and Turnbull were in power due to their respective parties' right wings, neither of which were representative of most of their beliefs. This helped destroy Gillard and is destroying Turnbull, because he is perceived as just a weak puppet.
The crucial thing I suppose is that you guys can't get rid of a bad president, realistically speaking.