No reason why you two can’t split the children’s breaks from school. What does your agreement state? If you don’t have one, I suggest you get one. If you currently have one in place, then I assume this means you want more visitation. Would your ex be willing to let you do this between you two? Write up a mini agreement modification? If not, then you’d most likely have to go to court for it.
We get my stepdaughter for the entire summer and we alternate school breaks and holidays. Maybe this is something you can look into?
You live relatively close to their mother so I see no reason why you two can't work something out. After all, this IS for the sake of the children...