It's a bit difficult to judge. Frankly, given that your wife is coming from the position of being a cradle member of the Orthodox Church and, therefore, entitled to - even required to - be accepted into the 'corresponding' Eastern Catholic Church, it's difficult to imagine that any Latin hierarch would decline permission for you to transfer canonical enrollment at the same time.
My recommendation would be to reach out to the Eastern Catholic hierarch/chancery/parish of the jurisdiction in which you're seeking enrollment and get their advice on how best to approach the matter. I'd start with the parish priest.
Your options, given your locale and the fact that each has a canonical presence in the US, are the Ruthenians, the Ukrainians, the Melkites, or the Romanians.
The respective hierarchs with jurisdiction where you live are:
Bishop John (Kudrick), Eparch of Parma of the Ruthenians
Bishop Richard (Seminack), Eparch of St Nicholas in Chicago of the Ukrainians
Bishop Nicholas (Samra), Eparch of Newton of the Melkites
Eparch John Michael (Botean), Eparch of St George in Canton of the Romanians
Contact info for all of these can be found here
The nearest parishes/monasteries to you, as best I can tell - including rough estimates of distance and drive time:
Annunciation: Homer Glen IL -- 3h, 150 mi
St John: Minneapolis MN -- 4.5h, 275 mi
St Michael: Milwaukee WI -- 1.5h, 75 mi
St George: Milwaukee WI -- 1.5h, 75 mi
St John: Northlake IL -- 2.5h, 135 mi
Holy Resurrection Monastery: St Nazianz WI -- 2.25h, 115 mi
St George: Aurora IL -- 2.5h, 140 mi
St Michael: Aurora IL -- same
Ss Peter & Paul: Chicago IL -- 2.75h, 150 mi
You can get at least some info - including websites, schedules, etc, on all of these (with the possible exceptions of the UGCC parish and Romanian monastery, both of which I'll add by the weekend), at the on-line directory