We share temp joint legal custody of 3 year old who lives primarily with me including weekdays. Can I enroll her in preschool? He won't cooperate.

If you already have a lawyer you should consult him or her.  If not, there should have been an order shortening time for a hearing so that the hearing could have been before pre-school started.  Without actually seeing the current court order, I couldn't advise you beyond this.

I am not admitted in California.  What is happening now is I hope not tell tale of your future dealings on these issues. But if it is, I would make sure that your lawyer knows that this is starting now and you need to make sure that it does not happen at every stage of your daughter's life.  Although you can not plan for every situation, make sure WHERE she goes to school (your county or your husbands, etc.) is accounted for in the order.  The fact that you work from home and have easy access to your daughter in case of emergency is a plus.

I am unsure how a judge will view the pre-school and I do see your point.  However, I would do nothing to possibly violate the terms of the temporary custody order or annoy the judge with accusations that you have violated it.   I would enroll her to save her spot.  Many little children do not like going to school at a young age and drop out for many reasons.  See what their refund policy is.  Then I would ask your attorney if he/she thinks you can make a temporary application to allow her to attend this "activity" in September.   As I do not really know what stage you are in all this it is and this is really not the place for advise, it is difficult to give options that are viable.  Only your attorney can advise you with any certainty.  Make the call.  Good luck.