Dear Our

Neither is any good, Anon, sorry. Use this:

Dear Guests

Dear (hotel name) Guests

Thanks, Mister Micawber.

What if I rephrased the previous example to say: 'Dear Our Child' instead of 'Our Dear Child'?

I presume that you are trying to compose the greeting of a letter, right? In that case, neither of those are correct, either. These are correct:

Dear child

Dear Sarah

In this particular case, just 'dear child' can be any child that is dear to the ones who address it, while 'our dear child' indicates a very close (possibly even parental) connection.

The question is about the informal use of 'our dear', or eventually the odd 'dear our', like in an e-mail, for example.

The analogy comes from 'my dear', which is

Not.

What about using 'dear' within a sentence?

That man is my dear father.

That woman is our dear mother.

Of course, those are fine.