Hi Claire,
If your homeopath was quite adamant in her response about vaccine, I can understand why.
Vaccines are dangerous.
Homeopathy is effective. Allopathy is suppressive (not curative).
If you don't fully understand the paradigm from which your homeopath was speaking, in reference to the damage that vaccines can do; and you say you come from a family of nurses and doctors; then take the time to read the links Simone posted and try to educate yourself a bit on what Homeopathy is and how it works.
You can go to
www.demystify.com and read a small booklet which you can download free, by Dr Jacob Mirman (he was an MD ---converted to Homeopathy). This is a very good starter for those new to homeopathy

.
There are many books you can source to gain a better understanding. If you would like other refernences - post back and I'm sure others will make recommendations for you.
As for personality, and the way you felt after speaking with your Homeopath. It's obviously hard to judge any of it, since none of us know you, her, or heard the conversation unfold.
Sometimes people feel uncomfortable when hearing something that is completely new to them and especially when it strikes against everything they understand (it forces one to re-think their 'world'). Making a shift in our thinking (comfort zone) is never done with ease

. If on the other hand, she was uncaring, and off-hand, then perhaps you oughta consider communicating your concerns with her. I hafta say, it's always better to bridge gaps than to run the other way having thrown a grenade behind you.
Just ring her back...tell her what you told us...and if you are uncomfortable doing that - figure out what made you feel that way. Were you being defensive (because you somehow feel responsible)? Are you just uncomfortable with confronting truth and would rather cut and run? Or, was she indeed being hard and unfair? Then decide what your best and most honest course of action should be (keeping in mind, that your daughter's best iterest should be the most important element in all this). Then just have the courage to do it.
Well, maybe I'm totally off course...but this is what came to mind when I read your post tonight. I wish you the best. And, if you have anymore questions - please ask...I'm sure others will do their best to help out.
Life; it's never straightforward - is it? Hang in there.