Definitely do not let your wife manipulate the situation. You have equal rights to your children, and if they want to go with you on vacation, then take them. I suggest you also take lots of photos with you and the children doing things together. Stay involved with their school, extracurriculars, and medical/dental appointments. Be sure the teachers know who you are and you know who they are. Don't let your wife push you out of these responsibilities. Be sure you have copies of important documents and photos in a safe place. Information is power. I suggest you talk with her about a separation agreement which provides for joint legal and joint physical custody, exchanging on a week-to-week basis, or some similar rotation. An attorney can prepare this for you for a very reasonable fee.
Sign up to receive a 5-part series of useful information and advice about child custody law.