Yeah, I guess I can look at setcookie() ; I am curious, though, because www.mysite.com is a name-based Apache virthost, and https://secure.mysite.com isn't; as near as I can tell in other types of operations, Apache treats them as totally different servers. If PHP doesn't, that'll be real good news.
Hopefully I'll have time in the next coupla days to get this tested and find a solution.
Thanks for your post...!!