Hi, you can't really be guided online because H&Cs are complex and unique to the applicant.
Generally speaking it seems that you may have a good application to present but it has to be presented well and maintained by providing information and evidence all the while you await a decision. Get a new job, children achieve something, whatever things happen that could possibly add value to your application should be submitted/added to your file.
Letters of support are good and you don't have to stop collecting them, get more and add them. Have you seen any news articles regarding your home country and your situation that you'd like the decision-maker to consider? Print them out and add them to your file. Did your children do something so demonstrably Canadian (it happens all the time) that couldn't possibly be repeated, built upon or furthered should your family leave Canada? You would know better than I what limits there might be for your children scholastically and socially should their lives be disrupted by leaving Canada (not simply medical stuff here). Do your children have letters of support from their schools, friends' parents, organizations or place of worship?
The Department outlines their key factors online:
- how settled the person is in Canada
- general family ties to Canada
- the best interests of any children involved, and
- what could happen to you if we do not grant the request.
Other matters can be considered as well, but take each one and write down what you have provided and as you find more material then submit it and add it to your list. Keep your own file and recall that these people will likely only see what you give them, they do these all of the time and they're looking to see if ALL of the stuff you've provided adds up to a positive decision.
Be clear, be concise, be realistic and be constantly updating your pre-decision application so that it remains current. It is a person making the decision and the ages, length of time in western education and the social adjustment of children to what is likely a more diverse range of opportunities in Canada are appealing because they advance the idea of them integrating into Canadian society seamlessly, and suffering a hardship should they be removed.
It is a positive thing for the officer to have concern that children not be removed from what has been an emersion into Canadian/western society and where the children are flourishing after this steady exposure. If someone has a daughter and she joins a club empowering girls, for example, this speaks to a core Canadian value. Girl Guides, or another positive social group would be an example of such a thing, I believe.
What works, what doesn't - H&Cs are hard to fiddle with so tell your family story in conformity with what the outlined factors detail, and have a bulleted summary of how you have tried to fit your facts into each of the factors. A "good" H&C is built in blocks of evidence under the Department's own outlined factors for consideration, and they are personal, kept well ordered and they are to the point.
Best of luck