I very much doubt they 'just get on'. She's tying herself in knots to get his approval and he is falling for it. I doubt she even likes the song - she's got a crush on him and has convinced herself you're not real or don't have a very good relationship with him and that's down to him. If he was telling her how much he loved you she wouldn't do it.
If he's not admitting it then that's because he doesn't want to lose the attention either. And he won't stop unless he thinks he is going to lose you and he doesn't want to. This is a bit of a game of cat and mouse TBH and would piss me off.
Call his bluff by either developing a 'crush' of your own (name drop some bloke. Talk about how he's so good at this, or did that for you. Such a great guy. Any woman who gets him is lucky. Etc)
Or tell him you want time out and are reconsidering. That the whole thing is just too suspect and has made you question whether he's the right man. You want to explore your options. You know nothings happened but frankly it's all made you think about things you hadn't before.
He's got you currently. He might be a bit less smug if he thinks he hasn't. I've seen many a man go from dismissive about them wife' to shell shocked, heartbroken, can't live without her realising what a prick he has been.
Comments about how they didnt seem to really be in love with her are angrily dismissed as just talk. Of course he loves her! I want to slap them for being so stupid as to be such a fuckwit in the first place but it's incredibly common.
Like it or not most men play down their relationships especially to attractive young women. One way to put a stop to that is to take away that relationship. Of course if he wants out it will backfire. You can have that conversation (keep it short! No heart to hearts please!!!!) and stay in the same house for the kids. It won't take long before he's trying to claw his way back in and at that point you say essentially youve been lying to her about me and it needs to stop.
I had an ex with a secretary that thought he was into her. He invited her out on his boat (he was really into waterskiing) she rocked up wearing a crop top with her equally silly little mate and got a shock when she saw me. It was harmless on his side but I told him to make it clear to her. Which he did. But we were quite new so he had no problem doing that. Yours is different.