Both are common. You need to speak to your lawyer. A forum can not guide your case without knowing any details. Either way having a Canadian child does not guarantee you will be able to remain in Canada.
Agree with canuck78 here.
But, if you are asking what the chances are for H&C for your case.
1. Medical ground: whose medical ground? Yours? In any case, medical grounds will only really be considered if there is no available medicine or treatment where you come from or where someone of your citizenship is able to go without issues. I don’t know what kind of illness you plan to use but I doubt that there is any kind that cannot be treated somewhere else. Too expensive? It’s still not going to be considered simply coz it is not Canada’s job to provide health care for people who are not Canadian, especially expensive medication.
2. Best interest of child - I’m assuming you mean the Canadian child? He or she is 2 months old. I find it hard to prove a baby’s best interest. As for the 5 year old who I assume isn’t going to school yet and has not established roots here, slim chance.
At the end of the day, if you need genuine protection and your claim was denied then it is either: a) the claim was found not to be genuine b) you failed to prove your case. As a parent, I wouldn’t put my children in a position to be in limbo for years only to be rejected in the end. So I hope you get good advice from an honest lawyer.