Hola! I live in Barcelona with 2 toddlers. Summer here is pretty awesome, the parks and beaches are full, there are festivals every time you turn around and, yes, you can take your kids basically anywhere at any time. Tolerance for kiddy wildness is pretty high although when things get to be too much, the fun often ends with a big smackdown. Depending on when in the summer you're here, there could be lots of organized activities or none... August is sacred and not much is scheduled. There's an anglo web page "kids in barcelona" that has tons of info about what's going on where and when.
As for breastfeeding/AP sort of stuff, while it's not the norm, no one, not even my Catalan in-laws, has given me a hard time about any of it and we're on the co-sleeping, extended breastfeeding, unschooling, cloth diapering end of the spectrum. And a little NIP means nothing here seeing as how everyone's topless on the beach and flashing flesh all summer
If you have specifics, feel free to send me a message