It is easier to completely skip the period when using pills than to make the period happen sooner.
The combination birth control pill is based on 21 active pills and 7 placebo pills. So, for the first three weeks, while taking the active pills, there is no period. On about the third day of the placebo pills, that is when the period happens.
To skip a period, you simply skip the placebo pills and start a new pack on the day after ending the first 21 active pills of the first pack.
This also means that to work, you need to start using the birth control pills at least one month before your vacation. You also want to be sure you are not going to have a reaction to the birth control pills. Some people are bothered by the side effects and some people aren't. One of the possible side effects is break through bleeding. Basically, that means you could have unexpected bleeding at any time if you happen to be bothered by that side effect.