WIBTA if I changed my ex’s headstone at his grave site?

My ex passed away. Everyone ((new wife and the two kids (27M | 22F) I had with him)) was fine with his mom taking his ashes. Our daughter wanted to visit his grave for Father’s Day. She saved up her money and bought a plane ticket to visit his mom and to see his burial site.

Background

After he died, his mom was in touch with all of us (new wife, kids, me, and his friends). She told me she wanted to bury his ashes so she could visit him. After a couple of months, she cut off contact with everyone. My daughter was afraid something bad happened and called the police to do a wellness check. Her grandmother told the police she didn’t want to speak with anyone.

She was close with my daughter so stopping contact was surprising to me. I understand people experience grief differently, but it got weird. We tried for over a year to reach her, phoned and sent letters. When we called the police again, they accused us of weaponizing them against her. We obviously haven’t done another wellness check since.

I went with my daughter to see her grandmother and dad’s gravesite. Her grandmother refused to open the door for her. We were there for almost a week and left her food and notes every day. We know she was there because her window was open. My daughter could smell food cooking. She spoke with a neighbour who cuts her lawn. He said she gives him money and sometimes cooks food for him. He had no idea she had grandchildren.

When we went to his gravesite, which took us over an hour to find because his mother couldn’t tell us where it was since she wasn’t speaking to us, we saw that she left out him being a father. His headstone said “Beloved son of (her name and his stepdad’s name).” There was no mention of him being a father.

WIBTA if I helped my daughter get a new headstone where everything is exactly the same except it included beloved “father”? I’m assuming it would make his mom irate since doesn’t want anything to do with her grandchildren. He was her only child.

Additional details:

Timeline - The last contact with his mom was a couple of months after his death. The Father’s Day we went to visit his grave and his mother was a little over a year and a half since his death.

His mom and my daughter have never had any issues. My son distanced himself from her when she played favourites with his sister.

My daughter had to travel over 7 hours to see her grandmother.