This is actually a fairly common occurrence with the Doctor. Considering his brash personality and tendency to be extremely rude, it's usually the Doctor who rubs Muse A the wrong way. All the same, bad guys and those without a strict moral background tend to rub the Doctor wrongly. Sometimes he's just dickish and won't want to be agreeable. He's this way in canon, too. His companion is almost always tapping him on the shoulder and reminding him not to be rude.
So, what do I do when my muse doesn't get along with another? Usually I just go with it. As people don't always rub each other correctly, I think it's completely fun to write it when my character has some sort of tension with another. It can potentially create fantastic dynamic.
Take eternityticking. Sylar is a vicious murderer, and when the Doctor first met him he hadn't fully split to the kinder personality that Gabriel now has. The disgust the Doctor held for Sylar created some of the most fantastic threads I have ever done with anyone. The dynamic between the fighting characters creates wonderful drama which in turn creates a fantastic story.
This was one of the first threads that Sylar and the Doctor did together. In the thread, Sylar comes to confront the Doctor for some of the things they've fought over. The Doctor moves him into a different room and, in the end, tricks him into going on a journey with him over the course of several planets. By the time Sylar leaves the Doctor they are not rubbing each other correctly, but they now have history and their own adventure.
No matter how much fangirls may ship them, the Doctor and the Master will never rub each other correctly (or that way, either!), and that's why we love to watch them on the show and that's also why I love to write them together. If they got along, they wouldn't be enemies, and every Doctor needs their Master!
One of my primary RP-partners is ambitious_woman. The two of us actually thrive on tension between our characters. In the relativespace verse, they're probably fighting more often than they're being adorable. Why? Because tension is fun. No relationship is perfect, and the fights make the adorable moments more memorable. One of my favorite threads with the Doctor and Reinette is a make-up thread they had after a particularly cruel argument. The fight itself made the make-up so much more important.
Dramatic tension between muses in wonderful. It creates situations that can later be re-read with a climax (sometimes!) and resolution (sometimes!). I thrive on the disagreeable nature between muses and I think that people should be more open to talking to other writers about having their muses dislike each other, because it can be very fun and create wonderful, lasting friendships between writers who work together!
Muse: The Doctor (Ten)
Fandom: Doctor Who
Word Count: 486