First question: where are you based?

Regarding Iceland: not sure about the weather in March, still quite cold, and Iceland is more a palce to enjoy outdoors.
As for Europe, there is no rain concept of rain season. Europe is huge, so you can get snow and cold in the scandinavian country, and enjoy a coffee on a terrace in the South of Portugal, Italy, greece, etc.

We travelled a lot with our first one, even while expecting the second one, generally not more than a few hours for the flight. As for the destination, it all depends what you are looking for.