This is something of what I imagined.
1. Vacation with your babysitters. Oh please do not think I am suggesting you take a 16 year old with you everywhere you go (unless, of course, that 16 year old is your child). Instead, Mr. Chastity and I usually vacation only with or to see family. This means we have built in care for the children, so we can get a few hours alone. If this isn't feasible, or at all attractive to you, consider vacationing with another family. Splitting the cost of a big cabin or beach house can often be affordable, as opposed to hotels. Then you can switch off with the kids. But in general, any extended vacation is easier if done with at least another adult - otherwise it's you and your spouse in an unfamiliar place with kids that probably haven't napped.
2. Tire them out. Make sure your vacation has plenty of time spent out-of-doors. Nothing wearies children like pushing their body to its physical limits: swimming, hiking, running, riding bikes. In my experience, kids are the best nappers on vacation because they are so exhausted from all the new activities and excitement. We usually try to spend the morning outside or doing an activity - sometimes I even let my baby skip her morning nap - and then opt for a long nap for everyone after lunch. Big kids can watch a movie or read, while younger ones really sleep. Either way, ample time for you to slip away for some time in bed - sleeping or not.
3. Location, location. If you co-sleep, beds hare, or have a couple of kids in your room with you on vacation, finding an appropriate place to get appropriately intimate can be rather difficult. Even if everyone is napping, what are you to do? With a baby, allow me to suggest no one is the wiser if you make appropriate use of the floor. After all, if s/he wakes up, they will not think anything is amiss when you bound up naked (the same, of course, cannot be said of a toddler). This has the added benefit of forcing you to be very quiet, which can be rather a fun game. If there are older children, get creative. Can you go on a hike to a secluded wood? What about a boat? Lakeshore? Boat house? Dock screened by large pine trees? Even the bathroom, provided the door has a lock on it. I am in no way suggesting you become exhibitionists, on vacation or elsewhere, but sometimes a stolen moment of intimacy - not a long relaxed encounter, mind you, but something a bit quicker - can be very satisfying and enjoyable. Maybe if it's quick enough you can make it back to the house for a sex nap before everyone else wakes up. (Sex naps being one of the greatest joys in married life, as far as I am concerned)
4. Have a sense of humor. Inevitably, when you have children, at some point you will be interrupted mid-sex. Sometimes returning to the glorious act will not be possible. This is truly unfortunate, the feeling which can be even more painful that holding in a sneeze. Prepare yourself for this possibility beforehand, talk about it and be of good cheer if it happens. Your spouse won't want to pick up where you left off if you're being pouty and rude and it certainly wasn't anyone's intention to spoil your fun. Try offering it up for a good intention and focus more on your spouse than on yourself - I am sure they were not thrilled about it either.
5. CoEd Bathing. Sex in the shower can certainly be tricky (I can write a post about that later), but it is doable. At the very least, sex in the bathroom itself is completely achievable, no matter your comfort level. If you have older children, time alone shouldn't be problematic; older and younger, maybe ask the older to watch the younger for 30 minutes; just younger, maybe wait until nap time or use those sitters that are hopefully just dying for some time with their baby cousin/grandchild/niece/nephew!
If none of these tips would work for you, and you know sex on vacation is going to be in short supply, the best suggestion is to have sex the night before you leave and make the vacation short.