Question: Following a previous discussion about **I would like** vs **I would have liked**, I have a similar question.

What is the difference between

> 
> I wanted to come to your party but I couldn't 
> 
> 
> I would have liked to come to your party but I couldn't.
> 
> 
>

Answer: 
There is no such rule: "our last week's meeting" is perfectly grammatical. There could be a last week's meeting that is not our: "the other team's last week's meeting raised the issue that we covering in our this week's meeting".

The phrase "in our last week's episode" is often heard in broadcasting, from native speakers of English.

The issue is that possessives don't always indicate possession. "last week's meeting" isn't a meeting that is possessed by last week; it just happened last week. That the meeting happened last week doesn't prevent it from also being our meeting.

Possession is exclusive. We can't have "Bob's John's pencil". The pen is either Bob's or John's. If there is a joint ownership arrangement with regard to the pencil, then this is expressed as "Bob and John's pencil". However, there can be a "Bob's carpenter's pencil". The second 's-word isn't a possessive; it's not saying that Bob owns a pencil which also belongs to some carpenter; the word "carpenter" here is a class, and the 's syntax indicates the pencil object's association with that class. That association is compatible with Bob owning the pencil, so both qualifiers can be applied.

Note that order is important; we would not say "carpenter's Bob's pen". The class relationship is applied to the pen first, then the specific ownership by Bob. There aren't pens which are primarily owned by Bob, and, secondarily, are carpenter's pens.

For similar reasons, we don't have "last week's our episode". We are not saying that the last week owns the meeting and so do we. If that were the case, it would be expressed as "ours and last week's meeting" (just like "Bob and John's pencil"), which is grammatical, but nonsense.

It seems that the time constraint "last week's" has to be applied first, and then the specific possessive.

What if we have multiple such 's qualifiers? How about "my last year's driver's license". This cannot be "my driver's last year's license" or any other permutation: the order has to be "owner -> time/space -> class -> object".
"Our today's meeting" means literally "(the) meeting of our today". This is why it's wrong. I believe we all agree that nobody would say "meeting of our today".