I don't have a problem with Burke confronting Sam, but there IS a time and place for everything. Burke had nothing to back up his accusations other than his word, and just whom did he think Maggie was going to want to believe, him or her father?
For Burke, time was up and patience was gone, and propriety was irrelevant. At this point, Burke was at a total dead-end with no weapon left in his arsenal but total confrontation and provocation. Push Sam off balance enough, and he might panic and confess. As far as Burke was concerned, I think, the more uncomfortable he made things for Sam, the greater the chance that he'd break, and spill everything. Confronting him with his daughter there might just have done it, if Sam hadn't fled.
Sam can prevaricate and stall
forever. He's proven that. Roger can keep the stone wall up forever. Honestly, I think the next step for him after this might be beating up Sam or Roger. I think he's got the sense not to, but he's going to come close. Burke's at a total impasse. He can't let that continue.