Preschool is for play, and learning through play. Pretty much, so is pre-K. It's for social skills and interaction and learning to work in a group and learning to separate from Mom and Dad in preparation for full days of school. It's not for academic instruction. So whatever you feel is urgent to "teach" your child, re-think that.
On the plus side, your child is getting some Spanish immersion at a young age, when young minds are little sponges able to soak up a lot of things. Learning a second language is an incredible gift, a wonderful boost for brain development, and a way to make all kinds of new friends. I don't know why you would object.
I'm not sure how you know that the teacher doesn't know the days of the week in English, and I'm not sure it's important for a 4 year old. So what is it that bothers you so very much about Spanish speakers? If the teacher can understand your child, there's no safety issue, so what other issues are there?
The fact that your child has a new sibling and goes with her dad 3 days a week tells me that there's plenty of upheaval in her life. Kids often have trouble adjusting to this. But we don't give in and keep them home for that reason alone. We help them be more resilient. Also, how long is she crying? Is it every day when you drop her off? Every time her dad picks her up and she has to leave school? Does it just last a short time? So maybe she has trouble with transitions? So many kids this age do. Some need a 5 minute or 2 minute warning before the next activity - that's very typical. So what can you and her father do to prep her for the changes?
Or is it that she is crying all day long, every day, throughout the entire school day? If so, has the school contacted you about this and have you had at least one sit-down meeting with the staff and with her father to learn more and brainstorm the triggers and possible solutions?
Sorry but without more specifics, it's hard to give you better advice.