Is the death of a girlfriend's father a reasonable excuse for a student to miss a class?
Edit: see below for some additional thoughts following OP’s revision of the question.
Let me start with this basic premise: Your students are adults.
Let me repeat that: your students are adults. That is one of the great luxuries of teaching in a higher education setting: you get to spend your time and energy actually teaching the subjects you are passionate about and not having to worry about being some kind of glorified baby-sitter or beacon of moral rectitude for your students. The division of labor is clear: the students get to make to their own decisions about how they want to best benefit from the course you are teaching, and you get to test them, give out assignments of various sorts, and give a grade at the end of the semester that reflects your assessment of what they learned.
And now for your question:
Is the death of a girlfriend's father a reasonable excuse for a student to miss a class?
While it is tempting to answer with a simple “yes”, I think the more accurate answer is that it is meaningless to speak about a “reasonable excuse”. Quite simply, in the context of a lecture-based college class, you should not be in the business of policing the reasons for students’ absences, or indeed whether they are absent or not. So in that sense, any excuse is a “reasonable” excuse. But if that’s the case, of course the notion of an excuse loses all meaning, so we come back to what I said above.
I know that what I‘m saying here flies in the face of the reality that some instructors mandate attendance in lectures, and that you do as well. Well, I have nothing more to say other than that such mandates are misguided and pointless, and lead to precisely the kind of fake dilemmas of the sort presented in your question, in which a baffled instructor tries to wrap their head around whether something is a “reasonable excuse”.
Finally, from a practical point of view, since you inherited this course from a colleague and don’t seem to personally have a strong attachment to the mandated attendance requirement, the best course of action is to simply drop that requirement, and free up your and your students’ time and energy for more productive uses.
Edit: OP has edited the question to clarify that the course is “conducted using a seminar course format rather than a traditional lecture format. For all classes except the first class, students present their work, and other students ask questions and give feedback and suggestions.”
For such a course, an attendance requirement may be logical. I’d still advocate for the instructor to make every effort possible not to get dragged into having to adjudicate questions about what is a “reasonable excuse” for missing class. It’s simply not a healthy situation for an instructor to be in and again conflicts with my “students are adults” premise. What I suggest instead is to have a policy that “students may not miss more than X lectures”, without making a distinction between “excused” and “not excused” absences, and to set X at a number that’s high enough that the policy won’t hurt students who had “serious” problems like an illness or a death in the family. For example X=4 or 5 would be pretty reasonable for a course of the type OP is describing. With such a policy, again the instructor will be treating the students as the adults that they are and freeing up everyone’s time and energy to let them do what they are actually at university to do instead of quibbling over bureaucratic nonsense.
Unless your university has an umbrella policy about absences, you as the instructor get to decide what you deem acceptable. In this case, I would first defer to what you wrote in the syllabus.
A common type of wording is to allow "excused" absences, where a proof of an excuse can range from things like a doctor's note, official notice from the university (commonly used for athletes), or an obituary, to name a few. If you were not explicit about absences in the syllabus, then you have even more freedom to make a judgment call here.
If the student experienced the death of an immediate family member, there's no question to me that this would be a reasonable excuse for missing a class.
What if the death was a student's guardian? How about a childhood friend? What if it was a cousin that they have not spoken to in 20 years but is still considered immediate family? Often, instructors ask that the student provide proof of the event such as by providing an obituary, which is what you could do here to avoid being an unfair instructor.
Is the death of a girlfriend's father a reasonable excuse for a student to miss a class?
Yes.
Yes, this should be a reasonable excuse.
Leaving aside the discussion in certain other answers about mandatory attendance policies and whether or not they're appropriate, there is an important factor that you haven't considered: University students are adults. Adults engage in romantic relationships that have traditionally been formalized with marriage. As time has passed, however, increasing numbers of young people have decided to do away with formalizing a relationship as a marriage when engaging in a serious romantic relationship that, in previous years, would have been recognized as a marriage. Indeed, in many places, the government has put into place rules governing "de facto marriages" that cause such relationships to be legally considered marriage.
As such, if I was in your position, I would assume that your student was engaged in such a relationship, and treat the death of his girlfriend's father the exact same way that you'd treat the death of his wife's father, and thereby treat it as a death in the immediate family.