What's the English equivalent of "it's the master's eye that makes the mill go"?
Solution 1:
An English idiom, which is almost exactly what you've provided as a translation, is:
If you want something done right, do it yourself.
Although it's commonly used in English (and has become English in its own right), it apparently originates from a French source.
Per Wikipedia:
In Bruis et Palaprat, Étienne penned the phrase "On n'est jamais servi si bien que par soi-même", which has widely been translated as "If you want something done right, do it yourself", although the literal translation is "One is never served so well as by oneself".
Note that the source of a variation has also been attributed to Napolean Bonaparte, so the actual etymology may be in question.
Nonetheless, whatever its source, it (along with its variations) is a common English phrase.
Solution 2:
Not commonly used, but you have:
1) It is the eye of the master that fattens the horse and the love of the woman that maketh the man.
2) no eye like the eye of the master.
3) the master’s eye fattens the horse, and his foot the ground.
(Concise Dictionary of European Proverbs)
.. “The master’s eye make the fat horse”, “The master's eye fattens the horse;”
— all these various readings are equivalent in sense and import, all thoroughly intelligible, and as good morality as the first, and yet they are all equally distant from what we want.
(English Proverbs and Proverbial Phrases)
Solution 3:
A common term related to keeping ones eye on your financial wellbeing was
"Take care of the pence, (and/for) the pounds will take care of themselves."
[Early 1700's from William Lowndes (1652–1724)] at the same time a popular sentiment was
"Whatever is worth doing at all, is worth doing well." [Philip Stanhope, 1746]
which now becomes "If a things worth doing, do it well" and later that century
"If you want a thing done well, do it yourself." Napoléon Bonaparte (1769–1821)
I'm sure as a youth I heard but can not corroborate,
"It's a good shepherd (herdsman) that looks over (after) his flock (stock)"
So without a verified phrase I would say the nearest paraphrasing could be
A horse thrives "under the watchful eye" of its master.
However that's only substituting a part. The nearest full phrase in meaning to take control may be
"To take the bit between his teeth" John Dryden's The Medal, 1682:
i.e "Control your own destiny or someone else will." Jack Welch