"kindly requested" vs "requested kindly" & "provide with us" vs "provide us with"

I am a contracts engineer working in the construction industry in the Middle East. A part of my job description is to manage official correspondence with the client. I am not a native English speaker, but I think I do have a fair sense of language.
I often come across the following concluding line:

"You are hereby kindly requested to provide with us the missing equipment..."

I am aware that "You are kindly requested" is a polite way of asking but I personally think kindly had better be used for the addressee, as in "you are requested to kindly provide us..."

Secondly, I think "...provide us with" is correct and "provide with us" is lame. I need an expert opinion.

I would request that you kindly reply to this post only if you are sure of the answer by experience or qualification.

"You are hereby kindly requested to provide with us the missing equipment..."

Yes; flowery politeness. The type of padding that is common in corporate correspondence. It's fine though.

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but I personally think kindly had better be used for the addressee, as in "you are requested to kindly provide us..."

"you are requested to kindly provide" is not, IMO, a good choice. It is better as is. The asker is stating that they are 'kindly requesting' (which is polite). The suggested edit is asking the receiver to provide, kindly - to provide something in a kind way. The original text may be overly polite, but the suggested edit is condescending, which is not what you want.

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Secondly, I think "...provide us with" is correct and "provide with us" is lame. I need an expert opinion.

Yes, "provide us with" is correct. "provide with us" is a non-standard construction.

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I would request that you kindly reply to this post only if you are sure of the answer by experience or qualification.

American, native speaker, writer/editor, business person.

To answer your second — and easier — question first:

… provide us with is correct
… provide with us is not 'lame' — it is plain wrong!

As regards the first part of your question:

You are kindly requested …

As you correctly say, this is intended to be polite, but the kindly is in the wrong place.

You are requested to kindly provide us …

This has kindly in an appropriate place, as @AndrewLeach has indicated in his comment.

Personally, I suspect that this question touches as much on cultural issues as on language issues. As a Westerner (UK), I would characterise this language as "old-fashioned politeness" of the type that (in my experience) continues to be used (for example) in the Indian sub-continent. From my cultural viewpoint, I would now regard it as excessive over-politeness — but that is not to say that it doesn't still have a place in business cultures in other regions. With that background, only you can judge whether it is appropriate for your situation.

If I were wanting to write something similar — and still (very) polite — I would suggest:

We would be grateful if you would please provide with us the missing equipment at the earliest opportunity.

Still polite, but not excessively so:

Please provide with us the missing equipment as soon as possible.