They look at all 3 scored from all credit bureaus for the both of you, and they will throw out the lowest and average the 2 remaining for each person. If you do not need her income, they would likely not use your wife on the loan because her score is low. Find a very good and recommended lender to help you. Do not go with your basic advertising lender, but one with word of mouth recommendations for all loans.
The only thing I see that maybe hasn't been mentioned already is that if you're only using your income to qualify for the loan, then you can be the only person on the loan and they don't need to consider your wife's score at all. She can still be added to title even if she's not on the loan.
they take the middle score of each person, but they will qualify you as a borrower and co-borrower. whomever has the lower middle score is how they will underwrite you. In order to qualify for FHA, you will need to get your wife's score up if you want to borrow together. If you can qualify without her income/assets then her score is irrelevant.
Each Client has three credit scores. One from each of the bureaus. We take the middle of all three bureaus and that is the score for each client. In your situation it would seem as though your wife's score is a bit low to qualify. Is this the situation you are in?