I share both joint and physical custody with my x. My daughter is with him during the week. Is he allowed to go on vacation during the school week.

Well, that's difficult to answer now that children are attending school remotely.  If remotely, then there shouldn't be a problem for him to take your daughter.  This is such a "it-depends" question:  how does it affect your daughter?  Does her grades suffer?  Also, you do not state the daughter's age.  If a teenager and they want to go skiing when the slopes are not so crowded on weekends, you might answer "have fun but make sure you do your homework or take lessons with you." Judges differ in opinions.  For me (and I'm not a judge), I don't see this as a "major" educational decision as long as the child does not suffer.   It might be good for your daughter to enjoy time with her dad on vacations.  Vacations are always a good time to bond and something to remember for the rest of her life.  It would be nice and respectful if he asked you first if you had any objections.