Should you offer to help with things around the classroom and follow-through on it? yes. Should you help make sure your child is doing his best and completing all assignments? yes. Should you do things just to make her happy? maybe / maybe not. Just like any other relationship, if you are doing things that make you uncomfortable to create the illusion that you are in a good relationship - it will falter and your child will probably notice that the relationship isn't based on honesty, even if they don't say anything. If you have a problem with the teacher or a situation in the classroom, you need to talk to the teacher about it to make things better for the children. If the teacher is a problem then it should come to light. Of course, my experience is way different than many of the posters here - my kids attend schools where parents are seen as a vital part of the whole education process - and the line between school and home is rather fuzzy - rather than many I have read where basically it has been stated that the teachers and administrators believe their power overrules parents and they do not listen.
Just stay true to yourself and your goals for your children, and all children when developing a relationship with any educator. Then you should develop a relationship of respect with the staff.