You discuss it with your new wife and the two of you decide whether you want to fight this or get along with your new in-laws. It's your wife's decision. You cannot file a joint return without her consent (you cannot claim her as a dependent, at all).
If you decide to get along, you will each have to file as Married Filing Separately (MFS). Your wife will indicate on her return than someone else is claiming her.
If you want to fight it, you prepare a Married Filing Jointly return, claiming the education credit and everything your'e entitled to, and let the IRS sort it out. Based on the facts you describe, they will rule for you. Your e-file will probably be rejected, so you have to mail in a paper return.
See this post, for a full explanation of when the parents can claim her. You may want to show this to the mother to show why she can't do what she thinks she can. https://ttlc.intuit.com/questions/2938663-can-i-claim-my-daughter-who-got-married-on-december-19th-2...
