They could in theory realize that someone just exited from the validator pool, those coins were sold on an exchange and then someone applied as validator with the exact same amount of coins.
They can realize that some funds are gone, and about the same time some funds are staked. At that point and further, any conclusion is fundamentally flawed, and any action taken is irrational.
I do think it can know that you're voting, by just running two nodes and checking the other blockchain.
But, that would make their blockchain reliant on forks, which nullifies the whole fork concept; a fork is a split, not a merge. Being able to fork is being able to oppose. If you charge forking, then your project is not able to fork, because forking happens by nature unquestionably. At least if we're working in a really decentralized manner.
Instead of penalties, the founders of the first chain (if they're so obsessed on disincentivizing the new chain's usage) should work on arguments. Nobody's going to stay in a anti-freedom chain when the neighbor-chain is in favor of them, unless they're morons.