Stepparents have the same right to claim a dependent as a biological parent, so either you or your wife can claim the child.  She will need to give the ex a signed form 8332 releasing the exemption.  The ex does not, however, qualify for EIC or head of household status because those are reserved for the custodial parents.

In the turbotax interview, your or your spouse would indicate that you had custody more than half the year (pick 7 or more months, not 6), that you do have a legal agreement with the other parent, and that you are giving them a release form.  The child will be listed on your tax return as a "non-dependent".  Whichever of you or your spouse is not claiming the child should not even list the child at all.

Having a "non-dependent" allows a taxpayer to qualify for earned income credit, the dependent care credit, and head of household.  But those three benefits are not allowed to taxpayers filing married filing separately.  I think the only conditions where you would actually get a financial benefit from listing the child as a "non-dependent" is if one of you had a dependent care FSA, or if the child is in college.  So you may not get any financial benefit no matter which one of you claims the child.  But it is the correct procedure when sharing custody.