Destiny... Welcome, lots of info here, you found the right place
As lonely mentioned... If you do submit without all required docs, do write a note explaining why... During first stage processing they will also reject an incomplete application... This is discretional, but if you have no documents and no explaination they might just boot it right back to you...
Here is my bigger concern,
Edit and I just reread and you state that the other daughter is from a previous relationship, so not all this applies to you, but might help someone so i will leave it and you can take what you need from it
and it might be an unfounded one... What is the actual relationship btwn his adopted daughter and him... Is there still a family relationship (niece, cousin, cousins daughter or something of the like)? If so theres a grey area that gives CiC rights to decline applications on what they call "adoptions of convenience"... This covers adopting family members to bring them to Canada when there is isn't an intent to develop a "parent child" relationship with that child, but rather the goal is just to give a child in the family a better life
.. It would usually be applied when the PR application covered the adopted child alone, but I'm thinking they could apply it to a spousal case, if they wanted to (I am not 100% sure, but id put nothing by them!)...
If the child did happen to fall under that category, the entire application would be refused and it would become very hard for him to reapply with that child on the application again...
For this reason I'm suggesting two things(if this is infact the case)... 1) try to wait out the adoption and gather (and possibly include) any evidence that the child is indeed in his custody and/or 2) engage a qualified legal advisor to help make sure you've covered your basis...
If he is in fact already the childs legal guardian and has a "father child" like relationship with her, you don't have a lot to worry about regardless of the nature of their family relationship (ie even if she is a neice or whatever), just be prepared to prove this if they ask.... however if he is not I would think you need to prepare well and move as much of the child's "business" over to his name/address (school registration, any other official paperwork) in advance... Especially if the adoption isn't finalized before the app goes in as they might wonder why this adoption is taking place at this time and investigate further...
While I hope the whole adoption area doesn't hold your application up, I would be prepared to produce information to support the father child relationship... Kingston is very unpredictable and this is the first case I've seen personally of this nature across these boards so I can't give you any precedence as to what they may or may not do, just give warnings of what they could do!
Sorry for the ramble, I hope that helped some!