Grammatically speaking, no, it is not correct, because in the language I grew up speaking — Twentieth Century American English of the Inland North variety of southern Wisconsin — you cannot write:
- *I request you to do something.
- *I requested him to be here.
You must write:
- I request that you do something.
- I requested that he be here.
Or much more likely:
- I asked you to do something.
- I asked him to be here.
Because request is one of those verbs that wants the other kind of construct, the one with that and a clause, not the one with a to-infinitive the way ask is. These are not always interchangeable; it depends on the verb that governs them.
Note that you can request NPs just fine; it is VPs where you must be careful.
- I requested his presence.
In my language, ask and request are different in what they accept as a complement. You cannot “request” someone “to” do anything; you can only ask them to do it.
See how that works?
While this restriction is not something universally applied by people long ago and far away, the ungrammaticality within the lect of standard American English as described above remains. The other form sounds foreign, as from a non-native learner of English who learned it from someone who didn't know English very well, or perhaps from reading dusty old books from authors several centuries dead.
In other words, it just isn't said or written there now. Remember that “ungrammatical” just means that it sounds wrong to the native speaker making that pronouncement, just as “grammatical” means that it sounds ok to them. There are also acceptability gradients between those.
What you won’t be able to do “prove” that something is “correct” or that it “not incorrect”. All you can do is document use and non-use, acceptability and unacceptability.
No one I grew up with, whether friends or family or colleagues, ever puts things together like this. It sounds “funny” to me, something I could not say and cannot say. That’s why it’s ungrammatical to me.
Here’s some supporting documentation for that use and non-use, courtesy of Google Ngrams:
As you see, the request you to style peaked in 1830 and has dwindled to nearly nothing since then. By the time something gets that rare, it’s bound to seem ungrammatical to people hearing or reading it, since they virtually never do so.
The UK version shows the same general trend, but with differing final results:
The fancy formal "subjunctive" version has not outpaced the older version in UK usage the way it has in American use. This may be because UK use of the "mandative subjunctive" (also known as the uninflected bare infinitive or the "modally marked" form) is quite a bit less common than the US use of that type of construction.
As for politeness, we don’t really do much in the way of etiquette questions here. However, things like
- We kindly request. . . .
- We politely request. . . .
- We humbly request. . . .
- We respectfully request. . . .
- We earnestly request. . . .
are all frequently seen in formal invitations and such. They are in the “expected” format. As with all language of courtesy, you should not get too worked up over what each word literally means in these frozen, fossilized forms. They have become formulaic, so it is “what people do” on such occasions.
Note that another old formula:
- We request and require. . . .
is something different; it is in fact a demand, and sometimes a command.