Wouldn't that double the amount of the reported mortgage?

You may need to adjust the beginning and ending balances on the 1098 screen in turbotax to reflex "your share" and the amount of interest you paid.

While it doesn't affect the taxes or interest directly, there are limits on the mortgage totals allowed.  Reporting the total to both filing could cause one of the owners to exceed the limit.  Therefore, reporting half avoids that.

Are all four of you on the deed and the mortgage loan?

yes

I understand your concern and feel I may need to be corrected. Pub 936 says nothing against co-owning a second home and only that you may only report the interest you pay up to the allowed limit. In your situation, I agree that you only report half the amounts since you are only deducting the interest for that amount of mortgage. I will edit the original answer.