I think your confused about the terminology.
There is physical custody, and legal custody. Right now your court order gives you and mom joint physical custody, and I presume, mom has sole legal custody (therefore overriding you on the school issue). You want the visitation schedule to stay the same so asking for sole physical custody makes no sense. Sole physical custody is when you have the children all the time, and there is no or little visitation with the other parent.
So you want to change that and ask that the court order reflect joint physical custody...although it already should since you have a 50/50 schedule.
I understand you want sole legal custody, and I understand your reasoning. Wait for a senior to come back and respond...however most courts will grant joint legal custody which means you have to work things out with the other parent. If you cannot work it out...someone takes it back to court. Its unusual for a parent to have sole legal custody these days...unless there are special circumstances. Nothing you have described are special circumstances. Also, if you had sole legal custody, that still does not FORCE mom to abide by your visitation order, any more than if you have joint legal. The bottom line here is mom is violating the visitation order, and you should ask the court to hold her in contempt. Changing either physical or legal custody does not change that action...if either parent violates the court order, the other parent can take it to court for contempt of court order.
So I think you may want to stick with joint physical custody - as I suspect you have...and personally? you have to have a very compelling reason to change sole legal, or joint legal --- over to sole legal to the other parent. I would drop that request and make sure you have joint legal custody. With joint legal, mom HAS to consult with you about school issues, medical issues - JUST like you did with her.
So in court, I would make sure there is joint legal and physical custody, address the preschool issue in court, and that your court ordered visitations need to begin immediately.