Was the husband cheating on his wife?

That's the big question for me. Not if Streep took the pills herself (which is explained at the end). I am fascinated because I found William Hurt to be the most dis-likable character.

1. He is clearly jealous of his daughter's writing success. When she asks him what he thinks about her piece, he snidely brushes her off and tells her some BS about having "to reach"- something we later discover he tells all his students. Some posters comment this was because he was sad about Kate's cancer, so he was coping and drunk all the time. But this was a early scene at his birthday- before Kate's prognosis is deemed serious. So in reality, Hurt's character was really not the mentor Ellie thought he was. He was a big fake.

2. He clearly is cheating on his wife. The other students even mention this in a conversation. And all those car drop offs late at night weren't just from his male friends. That female companion surely wasn't just there to drink with him.

3. Streep's powerful speech at the end seemed to sum it up: "There's nothing that you know about your father that I don't know. Nothing." In a way, this indicates Kate is aware of her husband's alcoholism and (possible) infidelities. She is a devoted wife, and breaks down the foundations of a strong marriage to Ellie in a way unexpected; there is a strong pillar of angry strength erupting from Streep's character that Ellie and anyone else are not expecting. But this speech made me wonder if even with Hurt's cheating- whether it even mattered. Was he cheating on her AFTER the cancer diagnosis - or even before? The fact that Hurt seems so fake about everything with Ellie makes me feel that her impression of him when she was younger has been a big lie. He certainly doesn't know how to emotionally connect. When she confronts him about the infidelity in town, he angrily says he will hire a full time nurse. Obviously the response of a guilty party.

Anyone else have insight?