Your side chain needs enough nodes and hashing power to counter 51% attacks.

You're pegging your side-chain coin value to the main-chain, but your transactions, blockchain, basically everything becomes independent. It's obvious that in the case someone gets control over 51% of the nodes or hashing power of your chain, they could pick transactions to double spend, or through a sybil attack if they control too many nodes. Your problems are exactly the same of every other chain, with only 2 differences :

1. The initial coins you used to create the side-chain are what you would hypothetically call your "genesis block".
2. You can exchange those coins to main-chain coins at the designed rate when you distribute your side-chain coins.