Mickey's personal life

You must have missed those parts of the movie. Mickey talks with his wife on the phone twice. He even tells Roger about his family and why they don't come to the park. He says something like, "They want me to show them around NY after the game..."
The movie alludes to Mickey truly missing his family in the scene after Maris goes thru the kidnapping threat. Mickey is getting ready to leave and asks Maris if he wants him to stay over that night. Roger says no and Mickey says something like, "Yeah, I'd probably just be in the way." That's a self-pittying statement .... then we cut immediately to Mickey drunk in a hotel room calling his wife at 2:00 in the morning, (NY time?). He says he wants to talk to the boys, etc, etc,. He is missing his family. The last thing he slurs is, "I'm so stupid." and then passes out. The camera pulls back showing us the "real" man ... surrounded by darkness .... he is missing out on his kids growing up. As the camera is pulling back, his wife is chanting his name over and over and over .... she never stops trying to wake him ... symbolically is she trying to awaken him from the inebriation of fame? I think it shows that she never gives up on him.
It all leads to his statement during the argument he and Maris have in the movie the night he brings the woman you mentioned, back to the apartment. It's the night he hit the home run with a muscle injury, .... Maris screams at him, "...You're Mickey Mantle for Gods Sake." Mickey's reply defines his character. He says that all the men in his family die young, and that he is going to experience life to the fullest, before it's his time to go.
So the movie alludes to the sacrifice Mickey has to make to play ball, while it brings Roger's sacrifice to the foreground. They were opposite sides of the same coin in many respects, and both went thru the pain of separation from their family, and handled it in different ways. Mickey hid so much physical pain, one wouldn't expect him to expose his emotional pain. To me, and maybe I'm naive, the back story to the two men chasing Babe, is how these two men exist in a fish bowl and how they each face the issues in their own way. Mickey had to choose between a life with his wife and kids and the glory that came after the game, in the bars and clubs.

Mickey did not stay with his first wife until his death. While they were always close, she divorced him sometime after he retired. He was, I think, remarried. His boys, to my knowledge, manage his estate and have recently cut a deal with Topps trading card company to have exclusive rights to Mickey's imaging on baseball cards. Previously, from 1996-2005, Upper Deck company issued Mantle's cards. One of Mantles sons, I think passed away while Mick was still with us. Through all his wild days in New York and his drinking, Mickey showed his real courage when, knowing he would soon die, he tried to show kids who NOT to be like and became an advocate for organ donation. His last weeks were truly his greatest. No one can ever argue, however, how great he was as a baseball player. In my eyes, he was one of the greatest who ever lived, right up there with Mays, Ruth, Aaron and Bonds. He was super fast as a kid and could always hit. Mantle was to baseball what Maris was to being a family man and person. Roger was the true role model, but the New York fans and especially the New York press, just couldn't let him be a soft spoken family man from the mid-west. He was the true hero, in my mind. 61* shows how, what should have been the crowning glory in a professional baseball players career, turned out to be the proverbial albatross around Roger's neck. He always said how much more pleasant his life would have been if he never had hit those home runs in 1961.