You would go to the family court in the county your were divorced or family court that gave you last orders. You request a modification of
parenting plan (visitation) "mother requests the courts to grant vacation travel from xx date to xx date to xx country to visit family as the kids grandmother has been sick. Children have been to xx country in the years XX. Mother has communicated this to father and offered extra time before and after vacation. Mother will buy round trip tickets and has family, job, pets, and kids school here in xx state."
Call family court, ask where there intake office is and how it works there. Here there is no fee and if you go and sit there, they will type it up for you. Here paperwork is also online and you can do it yourself and hand it in. Some states have a small filing fee. You will then get a court date a few weeks after filing. Here it takes 3-4 weeks to get a date. You may have to have him served the paperwork (some states have sheriff do it). If you have to serve, you can hire a company to do it ($75 around) or have someone over 18 give ex paperwork and sign they gave him papers.
If you need to go now, call a lawyer and see if you can file an emergency hearing due to mother is sick and you want to take kids now to see her. Are you waiting until school gets out? Courts may tell you to go but leave kids with father to finish school.