OH GOD YES. I can see Shin crying... But only if something happens, because he's ridiculously stubborn AND tough.
But yes, I think a combination of both pushiness and proving worth would work. Shin is... He's very angry and touch and mean and all bad-boy-ish at first, but with enough poking(read: FORCE), he just kinda... Deflates. Like a whoopie cushion.
Nope. She probably wouldn't know what he is. She'd probably just assume he's a little cat demon, albeit a harmless one since he's just a cute little boy.