You will do. Just rent 2 rooms...
Maybe look at Booking.com
BTW what dollars are you writing about? AUS -US -NZ -HK- CDN or one to the others?
Also what time of year?

I just checked a few random dates for the Majestic Residence, Passeig De Gràcia, 69. The rate for a two bedroom apartment (sleeps 4), was a little over €300/night, late December through early January. There are several other apartments in the same price range or less available on the same dates. So, depending on your dates, you should find something in your price range.

If you can't find anything you like, your other option, as already noted by ribeirasacra, is to book two connecting rooms in a hotel as very few hotels offer quad rooms.

Citadines

Try the Derby Hotels chain. I've stayed in a number of their hotels and generally have found them to be stylish and a good value. A quick search on their website indicates that they have family rooms (sleep 4 adults) at the 3* Balmes, 4* Gran Derby and 4* Granados 83 in Barcelona. They have some hotels in Madrid but I didn't check to see if they have family rooms.

The Gran Derby is fine for 4 adults (two bedrooms). You'll have to flip a coin to see who sleeps on the sofa beds at the Balmes and Granados 83, but they are good options none the less and priced right.

Apartments.

Easy to find ones to rent short-term.

You don't say when you need the rooms but I just booked a 2 bedroom apartment in Barcelona and there was tons of availability for 2 bedrooms. The price was E80 per night.

Us dollars. and May of 2013.
adrienne where did you find those?

You might want to consider the advantages/disadvantages of staying in an apartment vs a decent hotel. If it's a week or less, I'd opt for the hotel, unless you choose an apartment with all of the services of a hotel.

Check in and check out times, when staying at an apartment, can be a real drag, especially if the owner/rep doesn't show up on time, or if you arrive and they are still cleaning up the mess from the last person who stayed there.

Here's the thread with my short list and there are some other suggestions as well. We choose the first one - Modernista B. The agency got right back to me with answers to my questions. Others on this board have booked Habitat apartments and they seemed satisfied.

http://www.fodors.com/community/europe/please-help-me-choose-a-barcelona-apartment.cfm

I also saw a thread with a wonderful apartment that has a terrace facing the cathedral. Have you looked at hotel/apartment threads for Barcelona? It certainly wasn't $700 per night. Perhaps $150 to $200 - I can't remember for sure. Pull up the Spain threads and take a look at what other people are saying.

I also remember people mentioned Hotel Pulitzer and it looked nice and reasonably priced.