ESPN will automatically sign you out of your account when you leave the site and then go into a competitor's fantasy site such as yahoo. I know this makes absolutely no sense whatsoever because it shouldn't be able to read your browser.
But trust me, it does happen, a couple of years ago when I played fantasy football on both sites at the same time, I would have to sign back into my account everytime I returned.
It's tedious, but it is very fixable.....I don't think you are being locked out at all. I could be wrong, but that part about 'you are not a member of this league' is what I used to get as well.
Try going to the second league again and look at the top of the page to see if you are signed into your ESPN Fantasy account. I am pretty sure this is the problem.
That way, we don't all have to go set up yet another team in another league.