Can anyone see the data I send between my two computers ?

No.

All data sent between your two computers is strongly encrypted before it is sent on the Internet (using SSL:Secure Socket Layer).
Only your computers have the keys to decipher the data, meaning that anybody getting hold of the data would not be able to decrypt it.

Vedivi has 128-bit Advanced Encryption Standard (AES) encryption built in. All data including screen images, file transfers, keyboard and mouse input and chat text is fully encrypted from end to end. The encryption key is unique for each connection. The access code itself resides on the host computer and is never transmitted or stored on Vedivi Online servers. For this reason, it is impossible, even with the most sophisticated devices, to intercept the data necessary to decode the encryption. Transmissions cannot be hacked or compromised in any way.