My (29F) ex?s (34M) daughter (13F) is trying to ruin my relationship with my fianc? (30M)

I met my ex?s daughter (Gemma) when she was 4 and we broke up when she was 9. I grew really attached to Gemma over the 5 years I knew her, since I would be the one to look after her mostly whenever she was with her dad, so I really missed her when we broke up. Despite having a bad break up my ex agreed to let me spend time with Gemma as neither of us wanted her to be affected by it. I usually see her at least twice a month until the lockdown.
My fianc? knew about this before we started dating and was fine with it. We got engaged earlier this year and Gemma has taken it really badly. She never mentioned anything to me and seemed very happy when I told her, but she?s been sending my fianc? nasty stuff on facebook including ?proof? I was having an affair with her dad. My fianc? blocked her, but she keeps making fake accounts to continue harassing him. I?ve asked her to stop multiple times and she insists the fake accounts aren?t her (it?s obvious they are). Last week she crossed the line when she threatened to report him to the medical board if he didn?t break up with me. My fianc? now wants me to stop talking to her.
We had a big fight over it where he basically said he couldn?t marry me if I chose to keep her in my life (he didn?t say these exact words, but it was obvious this was what he was implying). I don?t want to lose my fianc?, but I can?t just abandon Gemma. I?ve known her for most of her life and if I cut her off it?ll devastate her. I need advice on what to do.
TL;DR ? I?ve stayed in contact with my ex?s daughter post-break up. It?s never been a problem for my fianc? before but now that we?re engaged Gemma is actively trying to sabotage our relationship. She?s tried to make it look like I?m having an affair with her dad and threatened to report my fianc? to the medical board. My fianc? now wants me to cut contact with her.


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