If we can't trust the website giving commands into the hot wallet, [edited:]how can we trust that same website to collect and offer the hot wallet valid and intended commands to pull?
You never fully can trust it, but you can make it more difficult for an attacker by having the hot wallet independently check the incoming commands for deviations from normal patterns which could indicate the website has been compromised.
At the cost of requiring more manual human action you can add more safeguards, like requiring customers to pre-register their withdrawal addresses and transferring a list of valid addresses via sneakernet to the hot wallet every 8 hours. Now an attacker can't break into the website and send the hot wallet a command to withdraw all the bitcoins to some arbitrary address because that address won't be on the authorized list.