I'm not sure why you want to use public Ip's in the other data centre. You're cassandra nodes in the other datacentre will be accessible from the internet
Personally I would use private IP addresses in the second data centre, on a different IP subnet.
A VPN is your only solution if you want to keep your data private and unhackable, as it's tunneling it's way through the internet
A slow network connection will mean your data is not in sync in both datacentres unless you explicitly specify quorum as your consisteny level in your mutation requests but your database throughput will be affected by this.
You bandwidth to the second datacentre and the quantity of your mutation requests will dictate how long it will take the second datacentre to get in sync with the primary datacentre.
I've probably missed something but there are plenty of intelligent people in this mailing list to fill the blanks :)