I think there are degrees of desire, and that the greater the desire the more one is willing to sacrifice or "work" for it. With your particular example, it also depends on how much you are able to afford. If you cannot incur all expenses and can only afford to treat a few family members, there is not much else you can do and I don't think this inability to afford all expenses weighs against your desire. However, if you can afford all expenses but only want to treat a few members, I think your desire for a family vacation where everyone attends is not as great.
With respect to God's desire that all people are saved, one observation made in the Bible is that Jesus does not chase down nonbelievers or spends all of his energy to convert any particular person. He tries to make a person believe once of twice, and then moves to another person, another town, etc. One example is the story of the rich man, if I remember correctly, Jesus saw the rich man walk away since the rich man did not want to give away his possessions. Even when Jesus teaches others, including Nicodemus, He moves on without securing their faith.
So, while I believe God desires that all people are saved, He still requires faith and won't force us to believe. A lot of atheists argue if God wants them to believe, why isn't God easily visible. However, Jesus said blessed are those who have not seen, so this makes me believe that God requires this sort of faith. I am not sure if God pursues us continually if we don't pursue him, but He is always available when we decide to return. The way God desires is different from how humans desire, as we humans do not require faith and the issues we deal with eachother are different from salvation which for Christians requires faith.