DD1 went to preschool at a church last year from August-May, 2 mornings a week. She did okay, had some problems with me leaving and then in the spring it was a battle to get her up and ready in the mornings because she didn't want to go. This year, that preschool was not in the budget. I have found another preschool that we could afford. It runs 3 days a week from 11:30ish to 2:30ish. Problem is, DD tells me that she does not want to go. The spring semester runs early February through May sometime. DD would miss 4, maybe 7 days in March due to vacation. She is totally bored at home as we only had one other SAH friend and they are currently moving 45 minutes away. Storytime at the library is over until late January. I completely envision a huge fight to get her ready to leave the house and then a huge meltdown when we get to the preschool and it's time to drop her off. Last year, up to the very end, at least once a week she would follow me out into the hall after I dropped her in her classroom and I would have to drag her back inside. She goes to kindergarten next fall and that is going to be 1) early in the morning and 2) all day. I almost feel like she needs some kind of structure now to get her ready for that but I don't know if it's worth the uphill battle I am going to fight.

Re: Should I fight to send her to Preschool?
I wouldn't let her stop going to school for this. Next year that won't be an option, so I wouldn't allow it now either. That said, I would try to talk to her during a time you're not rushed or stressed and find out why she doesn't like going to school.
Is she okay once she's there and you're gone or is she unhappy all day?
I personally would make her go. If anything, just to get into the routine of going to school. She will only be going for 9 hours/week. Is there an earlier option?
11:30 start time is lunch and possibly nap. This seems like an odd time for preschool as most kids are starting to get a little tired and whiny.
I think you should send her to preschool. Sounds like the structure will be good for her and help her prepare for Kindergarden. Which like a PP said is not an option.
If she is difficult at drop offs you should try reward charts or some other form of positive reinforcement of what is expected at drop offs.