The first step is to accept that you can’t get her to do anything. And to go even further, accept that your way might not be the right way. It’s great that you want her to be happy, but how do you know some as yet unnamed man is the answer? And is there any evidence that she is unhappy now? The subtle difference in your attitude that will come when you get rid of the certainty that you know what’s best for her will give you the best chance of her listening to you.
And if you really listen to her, and only if she truly seems to want a nudge, then you do what any sitcom 20-something helping a 50-something get out there does. Edit her online dating profile and then go shopping together – to a peppy musical montage. For bonus points, encourage her to pursue new activities that make her happy.
What is this hobby? I’ll venture that my answer would be different for “reconstructing antique pinball machines” versus “literary analysis of the Kama Sutra.”
Nonetheless, if it’s a problem for you, it’s a problem for your marriage, and you need to talk about it with him. Make it clear that you’re not faulting his behavior, but he also shouldn’t fault your feelings – it bothers you that there’s a woman so high on his intimacy list, even if the intimacy is not sexual but in the form of time spent and common passions. And be honest with each other about whether there are holes in the way that the two of you connect as well. Might it be time for a new joint hobby for both of you?