Rustamjan,
I've revisited your original thread to remind me of your situation. I think there are 2 issues for you:
1. Being with your non PR daughter in Canada.
2. Sponsoring your non PR daughter for PR.
Sponsorship and the issues pertaining to the process due to the RO breach have been covered in some detail. Your focus now is really about 1. You can apply for a TRP. The process involves submitting a regular TRV application but with an additional cover letter stating that you actually are requesting a TRP because you intend for your daughter to remain in Canada with eventual sponsorship - visitors are expected to leave so normally there would be issues around inadmissibility. Note carefully the requirement to submit a $200 application fee.
The letter and detail to put in the application require significant thought and preparation. You need to emphasize the difficulties you are facing but more importantly those that the child has by not being with you. CIC give an overview of the
process which clarifies the 'exceptional' nature of the status.
CIC quote a
52 days time for processing visitor visas at Moscow. I expect double this timeline for a TRP application as a minimum. The visa officer will likely go with a 6 month TRP but you may be lucky and get a 12 month or 18 month TRP. The duration really doesn't matter getting one is what counts so the child can travel to Canada. Once in Canada and you get your RO back on track you can commence sponsorship. Note that inland sponsorship of minor children has historically gone via the H&c route which CIC quote as taking 30 months. You may want to go with outland sponsorship where you use the Moscow visa post to process the application. TRP extensions in your case would not really be an issue but make sure you submit them in good time. The possibility of visa post denying the TRP and the telling/influencing CIC to report you is also in my opinion a non issue...they already gave you a pass so why hunt you down again.
You may find your MP more helpful once visa officer has made a decision. At the moment he/she could take the view that you want him/her to go over CIC and he/she won't do this as it has political risk and its not his/her job to interfere with CIC's operational policy subject to due process being followed.
The TRP process can be tough and long...you may get frustrated but you must be patient and persevere. You seem to have good fortune on your side by having an already signed departure order cancelled. Hopefully this is the case with the TRP application. I suggest you go to the family sponsorship section of this forum and search under a generic 'TRP' and/or Temporary Resident Permit input...you will get some direction from others having faced similar hurdles irrespective of how these came to be.
On a final note its best for you and the child when in Canada not to leave until you each have PR Cards in hand. In your case further ensure you have a good buffer of days so this scenario doesn't happen again.
Good Luck