My child is being accused of doing some improper things via Snapchat, but he swears that he did not do anything, and he is the type of person who probably would not. The only thing the police are going on is the user account name and the IP address which supposedly connects to my child's iPhone. Is there any way that someone else could have hacked into my child's Snapchat account and did the improper things, or is the IP address conclusive that it is my child's iPhone? My child and the other communicator are in different states.
Snapchat keeps a log of all messages sent and their corresponding IPs, so they can easily tell who sent which message and from where.
If someone compromised the Snapchat account and sent some content from another machine, the IP address would be the one of the machine/phone from where the content was sent, or possibly the address of a proxy/compromised server/anonymization service such as Tor.
If attacker really wanted it to appear as if your child sent the content, he could compromise a machine on your home network and use it as a proxy to send the content (it will appear as coming from your home network connection and would be potential evidence unless you have proof someone else was at home or your child wasn't there when it happened).
In theory he could also compromise the phone itself to send the content directly via the mobile network, but in practice I'm not aware of any iOS exploits for the recent iOS 8.X versons allowing this kind of attack, so the only option would be to make your child install some specifically crafted malware designed to give the attackers remote access to the phone and root privileges (to break into the Snapchat app's sandbox and steal its session token, to be able to impersonate this app). Installing such malware is no easy task and is definitely an unusual procedure, and most importantly requires a jailbroken phone.