Idiom request:putting forth an effort but it isn’t doing any good
Herding cats is an idiom for describing exactly that mixture of illusory control and pointless effort. A more common idiom for expressing wasted effort though is beating a dead horse, but it doesn't capture the mindset of thinking you're making a difference the way herding cats does.
You may use the idiomatic expression in vain
If you do something in vain, you do not succeed in achieving what you intend.
(Collins)
The captain tried to control his ship in vain.