Hi
So this is what you will need to make your Conjugal application successful:
Proof of relationship with your Boyfriend - all chat logs, visits, phone calls, remittance slips, photos, screen shots. If you just acquired your PR, have you even visited your new BF? You need a good relationship history together, so scrape together everything you can get. If you haven't spent that much time with him I would suggest a visit to log some relationship miles and try and join your finances and lives.
Very helpful things can be joint finances, and for us it was really helpful that we rent a house together in the Philippines.
They took note of the fact that his ex-wife lives at a different address from him. Proof of his address and us sharing a house was provided with remittances from me to the Landlord, Envelopes addressed to him, and his ID to that address.
So in your case, you will have to prove very clearly that you are not together with your ex husband. If you have any paper proof of his unwillingness to let you have custody of the child this is very helpful.
We provided a bunch of lawsuits that his ex slapped on him at various times. The one that was cited in our GCMS notes on our file was a lawsuit for Concubinage. That basically proves that I can't live with him in the Philippines because I will be sued for adultery.. that can apply to you as well, and it's worse penalty for a Woman to be charged of Adultery than it is for a Man to be charged for Concubinage.
So any difficulties that you have documented with your Ex will help prove your case. The fact that he wants sole custody of the kids is a good example. They also cited in our GCMS notes that my partner's Ex tried to have full custody of the kids. It helped prove our case.
We also presented documents from a failed annulment and explained why it didn't go through (because his ex was making difficulties with it). As long as you can demonstrate the total un-cooperative nature of your Ex, it will be easier.
You will also need proof that he can't come to Canada to live common-law with you. I know it sounds a bit obvious because it's very difficult to get a visitor's visa. But a visitor's visa denial can be helpful.
If you ever want your kid to come to Canada one day, he has to be examined by the doctor with your application, even if he's not accompanying you. If he is not examined, he will never be able to come to Canada. If you have any relatives that could help get the kid for a day and bring him to the doctor it would be worth it.
Good luck! It's just the beginning.. we are all here for your questions.