As a matter of fact without Divorce Decree the Divorce is not valid. Now the First Husband only the legal husband as there is no such document for any separation. The second husband is illegal and he cannot claim any right. The Affidavit is not at all accepted in case of separation (As a Divorce Document) in India. But you can confirm from your State Act i.e., Saudi Arabia.
Normally Absence of Positive Act documents will not effect the legality. (Without Birth Certificate we can prove our Birth (School Certificate, Affidavit, Without Marriage Certificate we can Prove. (Wherever we stay statement by any two witness can prove the Marriage)) But for Negative Acts like Death, Death Certificate is must and even if you prove, it cannot be considered as a Proof, like Divorce, it will not be considered without Decree.
There is no sanctity attached to the affidavit sworn in front of the notary public because your second marriage is void ab initio untill she takes divorce from the first husband. so this arrangement is illegal and void since existence. This affidavit is beneficial for you only as she shall not be able to charge you for the rape etc. How ever for the purposes of the maintenance you are not liable as this marriage is illegal until divorce from the first husband. More so there is no arrangement of such type in any personal law to be married like this on notarized stamp paper unless the marriage exists as per the personal law of the individual. Thanks