I think that spending quality time with your 4-year old daughter and ignoring your wife's STUDY PARTNER is an excellent choice. Just don't take her to see "Bambi"!;-) When around the study partner, only discuss firearms if directly questioned. She will likely have no questions since she may already know everything about everything (guns, politics, religion, science, etc.), and it has been my experience that such individuals are unteachable until they have had an epiphany.
Help your wife through this trial: She has it much worse than you do.
Note on study partners: In some things, the study partner can make or break your grade. For example, when I did my MBA, we had a group of 4 for a term project. The rule was, that the members of the the study group would assess each others performance. One individual felt that they would provide a significantly smaller effort than the others. After the project, we (the major participants), reported that the slacker only provided an 80% effort. We (three workers) each got a 95%, the slacker only got 80% of that (76%). The project was 80% of the grade. Since a C was tantamount to an F in undergraduate school, this individual was not very happy.