Kenczr,
Unfortunately Interval International does not make exchanges into Barcelona, but RCI (the other big exchange company) does. To get the Barcelona trade in RCI requires the higher membership fee level called "RCI Platinum". A regular RCI membership will only allow members to puchase rental weeks in Barcelona, but with the RCI Platinum membership (additional $79/year?) you can exchange weeks into Ona Living Barcelona. The timeshare is near the FIRA Barcelona Convention Center, in suburban Barcelona, but right on the Metro line. We have an exchange for 2 weeks there this summer through RCI.
Since you have already deposited your week with Interval International, do you have any friends or family members who belong to RCI and could put in an ongoing search for you for 2017? Maybe they could get the trade YOU want through RCI, and you could get them a trade THEY want through Interval International. If you did this, you would both need to pay for guest certificates with your exchange company to change the reservation name into the other's name. This is the only work-around I know of, but the challenge is that it is only safe to do this with someone you know & trust. What happens if you are able to get them their trade, but you are not able to yours? or vice versa. Sticky business, indeed.
It sounds like you are new to timesharing, and I regret to inform you -- but the trading your timeshare to exotic destinations throughout the world is not as easy as the timeshare sales people told you. It would be smart to read as much as you can about the ins & outs of exchanging here on the TUG BBS. Unfortunately, some timeshares are only with Interval International and others are ONLY with RCI, so it complicates things, although a few are with both.
Hopefully the week you own in Mexico is a prime season week (Jan/Feb/March), as that will have higher trading power with the exchange companies. Since most timeshares are NOT located in metropolitan cities, timeshare owners often need to rent their week, then use THAT money to rent accommodations. It is a pain, but there are TUG ads and rental sites that can help you do this. On the positive side, you can then rent exactly the time & place you want, which is not always so easy with timeshare exchanges.
Your easiest option would be to simply get a full week exchange into a timeshare resort in Southern Spain's "Costa del Sol" area (near Malaga). There is a large selection of timeshares and there is usually very good availability, especially if you put in an ongoing search for 2017 soon. Once you have a satisfactory exchange confirmed, then you could book 4 or 5 nights in Barcelona (Booking.com or AirBnB are good for units with kitchens) for either immediately before or immediately after your confirmed timeshare week. That would give you a little bit longer vacation, as well, because you don't want to travel all the way to Europe for a 1-week trip. It's way too short, because you lose a day to travel going, as well as a day returning. As for the best times to go -- I read that you want to avoid July & August when Spain is extremely hot and crowded.
Best of luck, whatever you decide.
--- Rene