Loyalty, now that´s an issue. My best guess is, put the low-loyalty troops under the command of a high-loyal general, provided you´ve got one, as far as I know, it´s the commanding general who determins the loyalty of the whole army (i.e. parts of one army don´t revolt - an army revolts as one, all or none). If you´ve got no high-loyalty general, you could try and, well, try the generals using a spy (alternatives are either assasinating or burning them with an Inquisitor) and hope for a better replacement.
Getting your King a higher influence helps as well, I think, usually it´s the loser kings who face army revolts.

As for the Alliance question, that depends. If you mean breaking as in attacking your former ally: bad idea. I´m not quite sure, but I think it loses your king influence and quite generally the others don´t take it very well, even the enemies of your new enemy. They like reliability. If you mean breaking as in choosing between two allies, I don´t think there are any penalties involved.