The post that preschool is a trend is obsurd, sorry. But preschool is a huge foundation for them. Teaching at home gives them no sense of learning to deal with peers, listening to a teacher and participating in a classroom setting. Preschool gives them this! Kids need to gain some independence and preschool is such a positive. 3 1/2 is the perfect age to start that!!! These moms that coddle their children and not allow them to grow aren't doing their kids any favors!!
Studies prove, kids do so much better in regular school if they have attended preschool. I see it with the boys I watch here. One never went to preschool and even being taught at home was way behind the others. So that statement is ridiculous. Preschool isn't a trend but it is a blessing it is state supported and there are so many out there to choose from! My daughter is two levels ahead in her reading due to preschool!
As far as the anxiety, it is normal.
All I can say is most kids go through this after being used to being home. Stand tough, though compassionate. You can sympathize with her and say "I know you don't want to go, but daddy and I think it is important and know you will have a good time" and keep going.
If she sees she can cry and you cave and give up then she learns nothing! Ask teachers on here and see how common it is. Now is a great time that teaches them that we may not always like doing something but if it is important we just have to do it.
The key thing you said in this post is she always has fun, so the dramatics are for the initial drop off. Continue to take her, let her realize that she has to accept it. If you don't what is she going to do in another year or so when she heads to Kindergarten? I mean kids may not like things, life is like that, however if she is really enjoying herself, you feel she is getting a good solid start to learning then I see no reason to just not continue.
Don't fight with her, be empathetic to her feelings but also remind her sometimes we have do to things we don't always want to. When she says "why do I have to go" answer with "I love you enough to want you to learn and start getting really smart"..and leave it at that.
My son did this last year he was 3 1/2 then too. The night before every night "do I have school tomorrow, I don't want to go"..and he would cry every other time I dropped him off. I just kept him going. He had a blast when he was there and I am a big believer preschool is really a positive for younger kids. It was hard to walk away when he was crying but I stuck to it, half way through the year he stopped. The worst thing you or your husband can do is linger! Just kiss and hug and walk off. Give her a sticker and kiss it to remind her of you during the day (that worked wonders with my son). But do not hang on to her and let her cry with you.
This year he started Pre K, he was so excited, loves going and not one issue. I think around 3 1/2 it is just a combination of being used to being home with mom all day and power strugggle.
Make sure she is happy there after you leave, that her fits aren't ongoing way after you have left and not disrupting anyone else. If not keep her going and be kind but firm about it has to be done.