The training Matt was referring to is/was called 'Aversion Training' or 'Aversion Therapy' - we used to use it for fear of snakes and the like. Others use it for fear of heights, water, etc. But, in psychology we have found some people to have unreasonable fears of animals usually due to something they have read, seen on TV or heard from a family source. We have also found that often these children/people do not actually fear the animal but instead come to use the opportunity to manipulate more attention to themselves - an attention getting mechanism. After all, they should be paying more attention 'to me than to that smelly dog'.
My immediate suggestion is not to buy into it and DO NOT change your life or your daughter's life sytle of having loving pets around for someone who wants more attention - that is just buying into the game. And please understand that children will come to actually believe they are frightened of animals when they may only be using that as a ruse to get more attention.
You said: I just hate for her to have to grow putting the animals out of our life when my niece comes over they dont live far so it is pretty often. My response to that is - don't do it. Your pets are as much a part of your daughter's life as any other aspect. Don't change you family's life just for one child (or her parents?
, hmmmm) who want things differently. Your daughter should be the most important child in your life and if she loves her puppies and kitties, then she should enjoy them and not be made to feel as though either they or she has done something wrong to exclude the pets when the neice visits.
Just my two cents worth here. Mikey.