From an outside perspective, I would answer your question RE: 2 wives as this: the way to live a righteous life is to not have 2 wives, and if you are Christian, you should know this. If you've gone ahead, and done this anyways, (we all sin) then I'd say divorce the second wife, and keep the first--as your vow was to her, and the second marriage would be invalid in the face of your vows. Honor your word. If you have children with the second wife, then you would have obligations to them, but to not see your former "spouse" outside of parenting roles.
If you're looking to the Bible for specific passages, I believe there are some about the "2 become one flesh"
I specifically brought up Catholicism because they are about the only Church that really cares about Annulments (CoE technically has them, but doesn't really utilize them, and so do Methodists, but again, it's not central to the Faith), and thought it was a relevant answer to your Annulment question. I think I explained as well as possible the value of having the Church review your marriage, and determine if the marriage ever actually existed, if you are of the kind that think "till death do us part" actually means what it says. As an individual, who has a stake in the divorce, it would taint your judgement, and so it is best left up to people steeped in scripture, and who can try to offer an objective view. (Btw, fun fact: the RCC actually has 2 councils review your marriage, and both must approve of the Annulment for it to be granted. If one agrees and the other says no, a third council reviews and makes the final decision)
i know a guy who actually married sisters. they had the same wedding ceremony. he married the other sister because she could not conceive children after having a hysterectomy due to cancer. his in-laws were ecstatic when he asked to marry them both. they thought the barren sister would never get married. a barren woman is not marriage material in their country. he originally just intended to take care of the barren one and provide a comfortable life for her, but it was difficult for her to accept that she would never have a husband in every sense of the word, so yea... he now dates both of his wives and has sex with them. his wives are quite happy with the arrangement. I would be hard pressed to find anything unrighteous about his decisions. what would really be unrighteous would be to tell him that he has to cast off one of his wives, seeing as they both love him.
so far as two becoming one flesh, its also stated that anyone who has sex with a prostitute becomes one flesh with her. 1 corinthians 6:16. from what i am seeing in the bible, nothing indicates that either marriages is invalid. the bible seems to say "dont do it", but seems to recognize that even if you do, its a valid marriage.
i know the catholic church has stated that anyone converting to christianity must cast off all but one wife, but is that found anywhere in the bible?