Can Jane go ?

If I had to choose one, it would be #E. I don't see anything wrong with #B though. However, I am not an English expert.

"Was going to go" makes it sound like it has already been decided that she will not go tomorrow.

"We want her to come with us today" makes it sound like it hasn't been decided yet.

So I would not have chosen E. I would have chosen B. She can go tomorrow. We want her to come today.

Also, "when it can't be so crowded" should be "when it won't be so crowded."

B, C or E all work depending on the context of Jane's specific circumstances.