If you have blocks corresponding to two different hash functions, you have two options:
1. Have a single difficulty value, and hardcode a ratio between the hash targets. Then if you choose a wrong ratio one type will be more profitable than the other and be solely used.
2. Have two separate difficulty values, each computed by the time it took to find X blocks of a type compared to the desired time. To know what the desired time is you have to set what % of the blocks you want to be of this type. It needn't be 50/50 but that gives the most security for this application. Then the respective difficulties of the two types will converge to a point where they are equally profitable.
Or simply make both half's Independent. Currently the bitcoin block is signed by a single hash (well technically a hash of the hash). There is no reason some alternate design couldn't requires 2 hashes. A valid block is only valid if signed by both hashing algorithms and each hash is below their required difficulty. In essence a double key to lock each block. Each algorithm would be completely independent in terms of difficulty and target and would reset
Even if you compromised one of the two algorithms you still wouldn't have control over the block chain. IF the algorithms were different enough that no single hardware was efficient at both you would see hashing split into two distinct camps each developing independent "economies".