thanks for your answer but I think you didn't get my problem.
On my pc I've updated my client to HW expansion.
I've one account with the HW product code registered (not only the early access), and I can log in with it without any problem.
Also I've another account with only ARR product code and with this one I can't log in on my client, because it asks me an HW product code for this account.

I don't want to upgrade the second account to HW, so it seems that I can't play with the second account anymore if I've installed Heavensward expansion on my pc. I think it's impossible that I need a ARR client for the ARR account and a Heavensward client for an Heavensward account

I dunno if I've explained it correctly, I hope so