Against all odds I ended up being seen as the "cool mum" (yes, that's what she calls me) by my teen. My ex is busy playing Disney dad and taking the kids out every minute of every day he has them, but when they come to me it's the routines they appreciate.
What makes me cool, apparently, is the fact that I don't take myself or them too seriously.
I give them space when they want it (so the odd evening they'll just be upstairs on their phone/ tablet), but we have mostly fallen into a routine of getting together every evening to watch a TV show we both enjoy once the younger one is in bed (any box set will do there, really).
They have light chores, are expected to help with some bits around the house, but we also just spend a huge amount of time talking - I happily listen to the latest teen drama and offer advice, share some of the crap from my life and work. I help with advice on homework and the very odd test prep. I make sure the boring forms are filled in, dentist and optician visits are done, and we go to the library every weekend I have them.
We share a hobby or two, but do it side by side rather than together - but she asks for my advice and appreciates it.
I think the big difference is that they see me as someone they trust and who cares about them in a reliable fashion. Someone who doesn't judge too much. That makes them open up and see you far more positively, they engage more with you and you become more fun as a result. It's hard to explain, because on paper my ex is doing the better job at being fun.
Oh, it helps I have had the odd nerf gun fight involving her boyfriend, I guess, but that just developed, again, through chat.