Dougal wasn't putting on an act over his wife's death in Outlander
It would be easy to believe that Dougal put on a show in Outlander Season 1, as he learned about his wife’s death. That likely wasn’t the case, though.
It’s easy to overlook the things that you have until they’re gone. I believe this is what happened with Dougal. He spent his whole life wanting to be the chieftan of Clan MacKenzie and focusing on his needs, that he didn’t once stop to see what he had. Why would he?
He “only” had daughters with his wife. During this time, this wasn’t great. Having daughters meant having political pawns to marry off, but there was nobody to carry on the family name. His son with Colum’s wife, who was passed off as Colum’s son, was the boy to pass on his name. Dougal may have looked down on his wife for only giving him girls—back then, people believed women had control over the sex of the child—and discarded her.
Dougal felt the guilt and loss in Outlander
He certainly took his wife for granted. It was only after her death that he realized everything that he had actually lost.
Up to this point, he was having an affair with Geillis Duncan. In fact, she was carrying his child. They likely even had conversations about marrying if their spouses died, but this was all just fantasy for Dougal. He likely didn’t really mean it, but Geillis did. She arranged for her husband’s death, and then Dougal’s wife died shortly after.
He would have been full of guilt. He may have even suspected that Geillis had something to do with it. Then there is the feeling of loss and grief. Fueled with the alcohol, is it really that surprising that he lashed out? He was angry at the world for taking this woman from him, and he never really acknowledged how he felt about her. Maybe there wasn’t any romantic love, but he would have cared for her. It’s not like he hated her.
If you think about Dougal's actions after this. He saved Geillis from the witch trials, but he didn't take her in as his next wife. He discarded her after this, suggesting that he blamed her for the death of his wife but he wouldn't allow his son to die.
So no, I don’t think Dougal’s actions were for show. I think he felt the weight of the loss of his wife in Outlander.