I have an idea for a mobile playing card game that I would like to develop. I'm a seasoned business application developer, mostly C# and JavaScrip...
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Given your background, I'd say you should try out Unity. That would let you code primarily in C#, create something that's cross-platform, and you could do it for free (buy a license only if you get to that point where you want one) and there are a lot of tutorials and community support.
You do still need a mac to publish an iOS app, but recently AWS launched mac mini instances, so you might have a way forward. I haven't looked into it personally.
Probably the oldest cross-platform toolkit out there is Xamerin/Mono. I've never used it, but its been around forever.
If this is for fun, then pick whatever gets you excited and who cares. If you really want this to have good shot in the app store you will want to think a bit more about which platforms to target more specifically, design, and assets. Mobile is mostly a design problem.
Cross-platform in mobile has always been a "mostly" true thing. They can get apps to run on both platforms, but its hard to give a correct experience to both and maintain both. Nothing to worry about to begin with, but I don't want you to think you can assume a cross-platform framework solves everything.