The way I see it is that if you really are not keen on Call Centre 2 then say no, irrespective of whether or not you get another job in the meantime. It's very unprofessional to accept a job then keep on applying for others in the hope something better comes along - and if you accept No. 2 then give your notice in in a couple of weeks' time, it's going to be really bad for reference purposes. A new employer always wants to know why you left the last job and will no doubt ring #2 and ask them - and this just makes it looks as if you might flip from job to job after a few weeks, always looking for a better deal (which tbh isn't always there when you get there).
If you go for #2, IMO, you need to be prepared to give it a few months at least before looking elsewhere. #2 are holding on for you, and no doubt there were other people in the queue that they could offer that job to if you decide you don't want it.
Don't play games - just tell them yes, and stay there and stop job-hunting for a while, or be honest and say no, then keep looking. It's not fair to anyone to keep people dangling like this, and does your own professional reputation no good. You applied for it, after all, you did your homework about their reputation so you knew what you were getting into.