You don't like the 2nd grade teacher. That's not going to change.
You don't know who the 3rd grade teacher is, right? Unless this is such a small school that there is only one class per grade? You seem to be sure that your daughter will have the same teacher in 2nd grade. So, no, if there are other classes, you can't go talk to anyone now - the teacher won't be assigned until June at the earliest, and August at the latest. And if you think that going in and laying out the deficiencies of her colleague is going to endear you to her (or that she will even sit and listen to it), you're going to have a very tough time of it through elementary school. As was said below, don't be that kind of parent.
I think you also need much more information about curriculum before you engage in supplementing. You seem to have the idea that workbooks and drills are the way to teach children skills, and to make them "love" school. You also seem to have a very high focus on testing for "gifted" students and I'm wondering if this over-testing is causing a problem. Even talking about "passing" such tests is really so unusual, I don't understand it at all. You have, no doubt, let your child know that you don't approve of his teacher or her methods. Do you think it's possible that he doesn't like school for that reason alone? There are so many ways to learn, and therefore there are many ways to love learning, but you seem to have certain methods in mind only. You want your child to have specialized teaching for "gifted" kids but you are in a small school, expect separate teaching for your child apparently, and yet your home "solution" is workbooks? Why aren't you reading with him? Does he have his own library card and the freedom and encouragement to pick out new things on many subjects? Do you have a membership at the nearest children's or science museum, or the art museum? Do you go on nature walks and explore the things your kids find? Do you go to kids' concerts at the library or the local arts center?
I think you should take 6 months to do nothing but the above, and also let your kids have creative play time that you do not direct or supervise, so that they can develop problem-solving and critical thinking skills without adult involvement.
My son grew up with a boy from another school system, whose mother was a teacher and decided that her brilliant children should not be doing the "busy work" homework the teacher assigned. She critiqued the teacher openly and her kids grew up very arrogant. She pushed one ahead by several grades, and he lacked the maturity to get through college admissions at 16. He had a miserable childhood, and now, at 27, he is just starting to find himself as a person. Don't be that mom.