Each individual has to file their own gift tax return. So you and your spouse should each file one gifting half of the value of the house to your son.
Some of this gets into legal advice areas and we absolutely don't do that here. So, for tax purposes, it doesn't make any difference whether you gift it to your son before or after the divorce or to a trust or to him directly. Whether it makes a difference for your divorce at all is a question for your attorneys.
As I said, you will each submit a form 709 individually - there isn't a married filing joint version - to show these gifts. If the form is filled out correctly it shouldn't confuse anyone.
@jackkgan
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