Can bitcoin and altcoin co-exist in sidechain? If Yes, strategy
No, you cannot set the exchange rate between your private coins and the pegged coins, because you cannot issue the pegged coins yourself.

The chain the pegged coins come from do still keeps track of how many coins were moved out, and there can't be more that come back. That would violate the sender chain's consensus rules.

So say your sidechain holds 100 pegged BTC, and 100000 private coins. If these were cheap to create, people would immediately convert them to 5000 pegged BTC using your 1:20 exchange rate, and try transferring them out. However, only 100 BTC can move back, because from Bitcoin's point of view, that's all what exists. You get effectively get a "run on the bank", and the peg mechanism fails afterwards, because you did not respect the rule that you can only have as much pegged BTC as there are real BTC backing it.