The grammar is OK, it's just not the pattern that you think it is.
The complete sentence is
Honestly, if I must endure a long and tedious evening, I'd rather it be with you on date night.
The pattern isn't exactly the one you chose from the English Grammar Today page because of the "if" clause. The pattern explained on the site would apply to this sentence (same subject for the clause)
I'd rather have date night with you than go to the memorial service.
But the "if" part of the sentence changes things. If I must endure X, I would rather endure it with you than at the memorial service.
I would paraphrase it as:
I'd rather the long and tedious evening I have to endure happen with you on date night than take place at the memorial service.
You could say "I'd rather (the long tedious evening I must endure) was with you on date night." but it is a little awkward sounding to me because we're talking about something in the future. I will poke around and see if I can find a reference to explain it in more detail instead of asking you to rely on my intuition about it.