Do not want to discourage you and I fully do not understand what you are trying to achieve, but you should first read some more on SSL. It uses asymetric cryptography and can be used in various modes.
- In all cases SSL encrypts the communication and attempts to prevent man-in-the-middle attacks (that is someone inbetween client and server (read: your proxy) that would try to decipher and possibly alter the communication
- Server authentication: server has got the private key/signature that is used sign the communication to ensure it can be verified it origins from that server. Because you do not have that private key it is impossible for you to decrypt the communication in the middle AND re-encrypt it again so that the final receiver (PS3) still thinks it origins from the server. You can attempt to re-encrypt the data again with your signature but that one will fail the check against certificate authority (PS3 as every browser has got a list of trusted certificates of top-level certificate authorities (like VeriSign) and can use these to verify signature on other keys - read more about SSL and certificates and authorities)
- There is a mode when public keys of both server and clients are mutually exchanged before any communication - that way clients can ensure they communicate with proper server and server can ensure it communicates with proper clients.