In general, spring is one of the rainiest times in Europe, but in my experience weather forecasts are a lot more accurate about temperature than about precipitation. If I'm in an area where rain is fairly likely, I just carry my (hooded) rain jacket and a folding umbrella every day. I have learned that it can rain when no rain is forecast, and I can remain dry even if it's supposed to rain.
I haven't been to Europe at this time of year (though I'm leaving for southern Spain on April 8), but I've spent almost 500 days there since May 2015, and in all that time I have encountered 6 downpours. Only one of them was an all-day affair. Other rainy days just had fairly brief showers. I'm sure it will not be as bad as you are anticipating.
It would be a good idea, though, to have a list of indoor possibilities. Take another look at your guidebook to see if there are places you want to add to your list of potential destinations. You might also review the Things To Do list on TripAdvisor. Barcelona has lots of interesting museums.