I believe he did indeed have an affair with him...though the extent of what Randall felt for Jack is unknown. Randall was in the same situation, a gay man living in a small town, married to a woman, living a lie...Jack was very lonely and felt completely out of place with Lureen and her family from the first day. Look how uncomfortable he looked in the scene after Bobby's birth. He looked completely alone, not belonging with his wife, new baby, his parents-in-law. He loved his son, but he wouldn't lie...Jack truly didn't want to marry a woman or have any kids, he only did that because Ennis wouldn't come with him in 1963. Years later, he told Ennis that outright, Jack never wanted to live a lie, Ennis felt forced to live a lie because he was afraid, but Jack wasn't afraid...he was forced to live a lie because of Ennis. Jack didn't even try to move on till over a year later, when he goes back to Aguirre, and he can't find Ennis. It was months after that when he decided to go to Texas and meet someone new, hence the flirting with Jimbo, and then after being treated in that homophobic manner, he felt he had no choice but to settle with Lureen. But Jack never stopped thinking about Ennis and wondering where he was, and dreaming of the day he would see him again! He could never forget Ennis, and he never wanted to either.
Back to the topic of Randall...you can imagine how a person like Randall must have felt. He was living a lie too, feeling stuck with a wife and pretending to be something he wasn't, in that town, he finally met someone that could understand him when he met Jack, so they connected right away. This does not mean that Jack loved Ennis any less. It also doesn't mean that Ennis wasn't his true love...he was. There is no doubt in my mind that if Ennis accepted Jack's proposal, Jack would drop everything in a heartbeat and go be with Ennis. But year after year went by, and Ennis still refused to live with Jack. This broke Jack's heart, obviously. He started going to Mexico for the prostitutes out of that anger and frustration, but he needed something more. He needed companionship and love, which a prostitute cannot give him. Jack needed a real relationship, and so he was glad to meet Randall. It doesn't mean that Randall was a replacement for Ennis, but what else could Jack do, Ennis wasn't there for him. So he turned to Randall, because in Randall he could have a friend and a lover. I don't know if Randall ever knew about Ennis. I wonder if Jack told him. Some people who watch the movie seem to not like Randall. They see him as a homewrecker, the person that came between Jack and Ennis.
But I don't see him that way, and I don't blame him. He either didn't know about Ennis, and therefore didn't know that Jack was essentially married in his heart to that other man, or he knew about Ennis, because Jack told him. I think he might have...I know Jack was very heartbroken and he needed to confide in someone. So I imagine he told Randall about Ennis. But even if Randall knew about Ennis, that doesn't mean he was a bad person. He was lonely too, and Ennis was a thousand miles away in Wyoming. I know I feel bad for Ennis that Jack cheated on him...but I can never blame Jack for that, because I feel Ennis forced him into that hard place to be. There is no doubt Jack would have remained faithful to Ennis forever if only Ennis had accepted to live with him. Imagine if you truly, deeply love someone, and you think of them as your soul mate, but that person refuses to be with you all the time...imagine the heartache and loneliness, and frustration that causes. It is only human to turn to someone else for companionship and to confide in...it doesn't happen after just one moment, it happens after years, which is what happened with Jack. Jack didn't go cheating on Ennis the first moment, it took twelve years of Ennis not accepting his proposal for Jack to finally break and say I've had enough of this. Jack saw Ennis for two or three weeks out of a year...the remaining 49-50 weeks he was alone in Texas, sick of living a lie.
It is only human that when he finally met someone he could talk to, he started an affair with this person because he didn't want to be alone. I mean Jack could never stop loving Ennis. He felt very very hurt by Ennis, and the worst part was that he felt he couldn't even say it aloud! Ennis wasn't aware of how much he was breaking Jack's heart. That scene where Jack drives away in tears breaks my heart every time I watch it, to the point where I can't even watch it anymore. Jack was deeply hurt, and it was Ennis who was making him feel that way...imagine the one person you love most in the world breaking your heart like that. It's devastating. Jack hid so much of his pain from Ennis till that last meeting when he yelled at him and admitted to the affairs.
Then when Ennis collapsed in his arms crying, Jack hugged him and held him tight...because what could he do...he just loved Ennis too much. As for Jack's father telling Ennis that Jack planned to come live with another man, well that I do believe he told it just to hurt Ennis. It struck me as something very mean for the old man to say...he was basically saying to Jack. "Ha, you loved my son, and he told you he loved you...well he had others." He was basically telling Ennis that Jack was some kind of player, that just sleeps with people and moves on the next one. It was a terrible thing to say. You can imagine how hurtful that is to Ennis, especially since Ennis is a person who had suffered from low self-esteem his entire life, and had doubted Jack's love for him many times. To have this mean old man tell him that he was just another notch in Jack's belt was devastating. Fortunately though, he realized quickly the truth...that he was the only special person in Jack's heart when he found the shirts. I think Jack's father mostly said it to hurt Ennis, but the information did come from Jack himself at the last meeting, after the major fight with Ennis.
I think out of frustration Jack told his parents he was going to bring Randall instead, and the old man used that information to hurt Ennis. I don't think Jack had given up on Ennis or was going to leave him...Jack would never do that. And perhaps Randall knew this too. Perhaps Randall was soon to end the relationship with Jack because he knew that Jack would never stop loving Ennis. Or maybe Randall didn't want such a deeply serious relationship with Jack, he only wanted the affair and nothing really more. But Randall is a person that can't really be blamed, and while I feel for Ennis that Jack cheated on him, because it is very painful when the person you love is unfaithful to you...it's just the sad truth that Ennis's repeated refusals to live with Jack is the only reason that Jack cheated on him.