AITA for telling my wife to go and see her son before he dies?

My wife Sara (39f) has a son Vicky (20m) from her previous marriage. Because of the way my wife and I got together, there was a lot of strife in her divorce from her ex, there was a lot of tumult in Vicky's life and he was only eight at the time. For a few years, my wife tried her best and tried everything to help him but it was like the more she tried, the further away he got. It came to a head when he was twelve and she caught him trying to smoke and then he almost broke her jaw when she stopped him. After that, she stopped trying to force the custody and just let him stay with his dad.

When he was fourteen and we had our son, she sent him a message that his brother was born and that even if he doesn't want to be around her, it doesn't mean he can't love his brother. He just responded back with "Go **** yourself". She tried the same thing three years later when our daughter was born but got no response this time.

Well, two days ago she got a call from her ex and he was crying and apparently Vicky is dying. He has cancer and they found it very, very late and he's optimistically only got a month left and he's been begging to see her. So, I've told my wife to go and spend the month with him. She can work online from a month or take a leave or just quit if they don't understand. However, she's refused and she's used everything from work to needing to take care of our kids to even 'what if it's just a trick to hurt me more' as excuses to not go. At the same time, she keeps crying, muttering about thinking she had more time, ignoring our kids, looking at old photo albums of her and Vicky.

It came to a head this morning when I caught her having a breakdown in her car before going to work. I begged her to reconsider when I saw and she called me a ****ing ***hole for trying to push her into going. I know he's not my son and that I have no right over him but not going is tearing Sara apart, so AITAH?

Edit:

To everyone confused, when our kids were born are not the only two times that my wife tried to reach out and ask if he was ready to see her. It's just when our son was born was the only time that he responded. She tried up until his graduation when even his father tried to get him to invite her. She sent him money, presents and everything for his birthdays.

And as for when he struck her when he was twelve, he did so with a hockey stick and then kicked her when she fell. She forgave him for that because she knew what he was going through and he's her child but she decided to stop seeing him then because she didn't want her presence in his life to make him more violent. What if he hit another kid like that was her thought.

And to everyone saying therapy. Yes, she took him to therapy, she tried so much but he was non-responsive then.