Awolnation: I know in your situation it's probably not going to help you, but I know that if you have Gwent on the Xbox and on the Windows 10 store on pc, you can play against each other. However, Sony's stance on cross-platform play is a little bit more strict than Microsoft's. So I wouldn't hold my breath on it, but who knows, they might (hopefully) have a change of heart! :P
Sony allows cross-play with PC, just not other consoles.
vickyra: I play Gwent on the PC. My daughter plays on her PS4. We really want to battle it out - is this on the horizon?
PC to PS4 cross play is supported (based on the Gwent FAQ). However, it's only supported in public matches. You can't send a request to a specific person to play them, so it's kind of hard to have a match with someone directly. Friend matches are only supported for players on the same platform.