Jealous Girlfriend

I hope, this community can help me and give some useful advice. I am a man in his mid forties, father of two and in separation. About one year ago I met a really cool - though much younger - woman. Although I was in separation mode, I couldn't help but falling in love with her. I was not looking for this - it just happened, because I found a true soul mate. She is cute, she is fun, she is smart - she is everything a man can dream of. Except for one thing: she is ridiculously jealous. In the process of my divorce I have to appear in court again and again, and normally these sessions last several hours (the issue is money, what else?). Now, here's my problem: Eunice does not believe me that I spend all this time in court. She thinks I still have an ongoing relationship with my wife or - if not - a fling with somebody else. This is of course totally untrue. I love Eunice and nobody else. But she does not believe me! She even threatened to hire a private investigator. How should I convince her that my love is really true?