Personally, I LOVE my midwife's apprentice (okay, okay, I *am* my midwife's apprentice).
Really, though, it's perfectly acceptable for you to privately let your midwife know that you're just not feeling like you "click" with her apprentice, and that you'd prefer not to have her at your birth. I am one of three apprentices in the practice for which I work, and I know it has happened that a client has requested not to have this-or-that apprentice at their birth (bad personality match or whatever), and that's perfectly fine (and part of the reason, from what I understand, that my preceptor likes to keep several of us around
). When it has happened, I think my preceptor has handled it relatively delicately and diplomatically with us.
If a client didn't want me at her birth, I would really hope that she would just let my preceptor know--and the sooner, the better. It might sort of "hurt my feelings" or something, to be honest, but I would be really much more upset to find out some time after the birth that I was unwanted/unhelpful there.
And, for that matter, I suspect the apprentice wouldn't be *shocked* to learn that you didn't want her there--I think it's unlikely that she's feeling a really tight bond with you that isn't really there. I, for one, fancy myself a rather intuitive individual when it comes to these things, and I think I can usually gauge relatively accurately how clients feel about me (although, admittedly, you have me sitting here thinking back over the births I've attended--wondering which woman might have actually loathed having me there
So let your midwife know. She may still like to have an assistant there for the birth, so the sooner you let her know, the more time she has to find a replacement (and the fewer visits the unwanted-apprentice has to attend before learning that she won't be at the birth).
Another thing that might be possible--when someone calls in labor, unless they sound like they're pushing or something, my preceptor typically goes out to the woman's house and sort of assesses what's going on before calling me. When there are two apprentices attending the birth, which happens once in a while, she usually calls one of us out shortly after arriving at the woman's house, and the other in just enough time to make it for the birth. If you felt like it would be okay, perhaps the midwife could do something like that--just call the apprentice much later than usual, so that she wouldn't be there for your whole labor, but only at the very end, to assist at the birth, if it becomes necessary. Just a thought...but you should definitely talk to your midwife about feels best for you.