Regarding the cards; One is my industry credit union and the other one is Barclays Bank. I believe it's the Experion score they offer. It's not FICO, but it's usually within 10-15 points of my FICO score, so it gives me a good barometer for where I'm at.
Neither of these cards offer points so I paid them off and stopped using them for a while....and the score disappeared. I found that you have to place at 3 charges a month on the card to get the free score. I guess that's their perk instead of air/hotel miles. I was looking into switching my Barclays card to the Virgin America card they also offer and they told me I would loose the free credit tracking.
For the timeshare, you need a 650 score, so if you have anything over 700 with any of the agencies, I think you are safe to assume it won't be a problem to qualify.
The timeshare shop doesn't offer which agency they use for the checks. I would ask, but I just did that shop a few months back and am out of rotation for it anyway....