Second Amendment? Really? I hope you're joking.
I think that as a general rule, it's rude to show up at someone's house without calling (or emailing, or texting, or something) first. But there are exceptions. It all depends on the people, the relationship, the circumstances, the expectations, and occasionally the culture of the area or the social group. Some people are OK with unannounced visitors, some aren't. And the visitor has to be prepared to *not* be welcomed in with open arms.
I don't get any vibe from the OP that her relative wants to rekindle her relationship with her old boyfriend. She's in the neighborhood, she'd like to see him again, maybe see how he looks now and how he's doing, and offer condolences on his dad's passing. She mentioned "having a few laughs" about the old days, but she has to be prepared for the distinct possibility that may not happen. He may be busy, or ill. He might accept the condolences and the cookies and explain that he's not up for a visit, or he might invite her in to have coffee/meet the wife (if he has one).
Story 1: Years ago I had a guy I'd briefly dated show up at my door unannounced. He'd been the one to break it off, so this wasn't some guy who'd been pining for me or stalking me. His showing up was a very pleasant surprise, and we did rekindle the relationship, although it didn't last (his decision again).
Story 2: A family I've been friends with for going on 20 years moved into my neighborhood a few years ago. This year they moved in downstairs from me. We have a running joke between us that while their door is always open to me, I will not drop by unannounced -- unless UPS has left a delivery for them at my door -- because "I'm not Kramer."