Does a divorce take place and count as one pronouncement before Allah if a divorce document is issued for the second wife, without uttering the words of divorce, intending it, or receiving anything in return, with the aim of stopping harm from the first wife?

If you did not utter the divorce of your wife, nor did you write it with the intention of effecting it, then the divorce has not occurred. However, your continued presence with her despite the issuance of her divorce document is a serious matter. If you wish to keep her, then have witnesses attest that she is still your wife and that what was issued was merely a gesture of goodwill and an avoidance of problems, and not a divorce, in order to preserve rights and prevent corruption.