The old playbook still applies: the influence of the rainy season on travel planning has historically been less decisive than other factors.
We traveled like that for a long time, and experience shows that family constraints and budget are king.
Here in Italy, if the only time the whole family can gather is during a wetter season, but the ticket prices are reasonable, rain becomes a minor detail.
For example, during Easter holidays, weather doesn't matter much; if we can be together at an affordable price, that's what counts.