2 adults and 1 youn teen cannot share a room?

13 years old is certainly not a child and would require an adult bed. You pay by the body and you cannot have a hotel room where any number can crash in it. This is normal wherever in Europe.
There is many a hotel, or you can research using a directory like booking.com, which will give you rooms suitable for three when you input the correct detail.

Nope, not usually - a double room means 2 people. It's not a law, as far as I know, just the way things are done. I even ran into this issue with my 3 year old. 2 adults and a 3 year old often required a triple. It's a big difference from the US where a room is a room and number of people doesn't matter, within reason.

Some hotels will do a double with an extra bed - you pay a nominal fee for the extra bed. It will take a bit more looking, but you can find this. Try booking.com or other sources to find smaller hotels - the bigger chains may stick to the 2 rooms policy instead of offering an extra bed. Also, some will offer triple rooms, which are often not a ton more than doubles and certainly much less than a suite or 2 rooms.

Either 1) Request a Triple Room or Family Room at the hotel or 2) Change hotels to one that DOES have triple and/or family rooms.

As noted, this is very typical for European hotels and is very different from how US hotels usually operate. The reasons are several and include the fact that most rooms are much smaller and that charges are based on occupants. The question does come up frequently from those not used to the system. Know that you wouldn't be able to "sneak" anyone in either (not suggesting you were thinking it). It can actually be difficult to find single room accommodations for 3 people, especially in older hotels in the city center.

Thanks, all. Having to get a triple or suite is going to make it a lot tougher to find a space within budget in a good location, but hopefully we will manage. . . I've stayed (alone or with only 1 other person) in 7 hotels in 4 European countries in the past 7 years, so I know they are smaller than US hotels tend to be, but three small, related females could have been comfortable in any of those rooms I have stayed in. . .
To Neil: With all due respect, 3 family members (one of whom is a kid) is a far cry from "any number" crashing in a room.
If anyone from the Steves organization is monitoring the forum: this would be a good thing to note in the "Sleeping in. . . " section of your great guide books.

As far back as I can remember RS books described hotel situations - single, double & triple and then noted in the Hotel sections what each hotel offered. Is this not true anymore?

If you share your budget you might get some specific recommendations

Perhaps think about renting an apartment through air bnb or homeaway?

I =have stayed in several triple rooms in various parts of Europe,last week I was in Prague and had a twin room to myself but friends had a triple room for a couple.
I had a quick look at booking.com for Barcelona in August ,i just put in random dates for a 4night stay and got quite a few hits,hopefully this link will let you see what could be on offer.
http://www.booking.com/searchresults.en-gb.html?aid=303948&label=barcelona-AGZSgXKavIDZ_hWc5xuFGQS27319422381%3Apl%3Ata%3Ap12240%3Ap2%3Aac%3Aap1t1%3Aneg%3Afi%3Atiaud-146342138230%3Akwd-13314910660%3Alp9046887%3Ali%3Adec%3Adm&sid=10e033b1a3e349947af2a1a73375197b&dcid=1&checkin_monthday=8&checkin_year_month=2016-8&checkout_monthday=19&checkout_year_month=2016-8&city=-372490&class_interval=1&group_adults=3&group_children=0&hlrd=0&label_click=undef&no_rooms=1&offset=0&order=price_for_two&review_score_group=empty&room1=A%2CA%2CA&sb_price_type=total&score_min=0&si=ai%2Cco%2Cci%2Cre%2Cdi&ssb=empty&no_dorms=1&tfl_cwh=1

gallagher-thomas -
'To Neil: With all due respect, 3 family members (one of whom is a kid) is a far cry from "any number" crashing in a room.'

I clarified as best I could for those who might come across this in future....and 13 years old is certainly not a kid in Europe, so it appears we are divided by a common language.

It is true that in the US a hotel room is a hotel room. Many have 2 double/queen beds or a king size bed and a hide away bed in a couch. And even a single traveler gets the same huge room that 4 adults might get.

It just isn't that way in Europe. Most hotels actually have rooms that are sized to the number of people they expect to have sleeping in them. So a single traveler gets a room that is (barely) large enough for a single person and so on. While unfortunate for those who expect rooms like you get in the US, it is the way it is. The only solution is to reserve a room at the desired hotels that are designed for the number of people staying in it. This might mean some of the room cost will have to come out of your pocket if your company won't cover it. But that's still better than paying all of it yourself, isn't it?

It is law also in US. All lodging establishments are licensed for a certain number of guests no matter the size. My 6 room B&B was licensed for 14 occupants (I had 2 rooms that were triples) even though I had space enough for a roll-away in 2 rooms so I could fit 16. I could be fined or lose my license for exceeding these limits. If you look when you check into a hotel somewhere there is a posting for maximum occupancy.

Thanks again for all the input. Once I accepted the reality I had to work with, I started looking at lower-priced places in the neighborhoods I thought would be best in order to be able to afford a larger space and did find a few very nice options. It appears we will now have a giant suite in a Steves-recommended hotel (Banys Orientals) that looks beautiful and is well located. By "fun neighborhood" (yes, I know that is subjective) I meant an historic neighborhood close to sites and such, e.g., the Barri Gotic -- not, say, the business district or, in our case, a modern shopping-oriented neighborhood.

I still know that we would have been quite comfortable in a smaller place because I have no intention of hanging out in the room, but I'm sure we will enjoy the space.

Also, just to respond to some of the messages regarding the concept of capacity limits -- of course there are limits! But again, we are a family group of 3 small females; I was not suggesting bringing a football team into a double room, folks. Based on my own travel experiences, I personally feel the limits here are more stringent than they need to be, but . . . I don't make the rules. Thank you again!