What are the specifics surrounding primary custody to mom when the order also indicates joint legal and physical custody? Does that give mom any specific rights more than dad?

Basically the one with the non primary gets set visitations. Generally they are to be told about school, doctors appointments and anything significant that is going on.

If mom is the primary and there is no set visitation schedule, then mom is in control. However with joint legal custody major decisions need to be made jointly.

Any question on law needs to include your general local as laws vary by area. If you want to describe the specific situation we can better advise you.