I wouldn't use either of them.
1. The general commanded the Officer's Club be off limits to the new recruit.
My grammar books says the above is ungrammatical because we can't omit 'that'
after command. Is my grammar book right?
also,
2. The general commanded the Officer's Club to be off limits to the new recruit.
What about sentence 2? Are both 1 and 2 grammatical?
I wouldn't use either of them.
There's no need for "that."
She ordered the tarragon be omitted from the soup.
The Red Queen ordered Allice's head be removed.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
Ordered is a much better verb.
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I think that new recruits are not officers, so they should know not to go to the Officers' Club.
Regardless of the rest of it, the general didn't command or order The Officer's Club to do or to be anything.
He ordered that the Officers' Club be off limits to new recruits.
He ordered the new recruits to consider the Officers' Club off limits.
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.