The only Capcom character I can come up with and whose storyline I am the most familiar with is... *SIGH* Vergil.
I thought long and hard over this and I can't really come up with dubious relationships in Capcom's games. Capcom characters don't exactly sleep around as often as Marvel characters. Nothing of note in RE, nothing of note in SF, GnG, Godhand, PW, Strider or any of the other popular Capcom franchises. I came back to DMC and Vergil was the only one who fit.
I am going to pull a Capcom canon on your guys.... Vergil IS Nero's father. This was hinted at numerous times in DMC4 but never said explicitly. After DMC4's release Capcom released a couple of novels to flesh out DMC4's story. One of the novel had explicit mention of Nero's origin as Vergil's son, complete with him paying a visit to Sanctus and Sanctus calling out Nero's mother a "whore" (or maybe it was Vergil who called her a whore... can't exactly recall but the word whore/prostitute was used).
The relationship is dubious but it just barely fits the bill. I feel like even though he has given an indication that it might not be Marvel universe, I still believe that Marvel characters fit this bill more.