I don't know about Canadian parental right laws. I HIGHLY advise you to see an attorney about your rights - especially concerning the child as you are not the biological father.
Here in the US, you would likely be advised that you have limited (if any) significant parental rights. An overwhelming advantage is given (whether warranted or not) to the biological parents. I fear that if this other man demanded to see the child and choose to pursue it in court, you would lose. If your wife leaves you, I also fear that you will have little to no rights where the child is concerned. But here's the thing your wife has not seemed to have considered. Since you are NOT the biological father and did not willingly choose to adopt another's man child or enter into a binding legal agreement to have another man father a child on your behalf, I think there is a pretty strong chance YOU aren't responsible (legally) for any child support. AT MOST, you may be liable for spousal support. However, even that is not certain because of her betrayal - especially with passing off another man's child as yours. There is a good chance she would get next to nothing and need to sue HIM for child support. Your feelings for the child likely complicate this substantially. I can only imagine that in all the time you believed it to be your child, you bonded closely. Parenting a child and being family is not limited to blood. Love and care build equally, if not stronger, bonds. Unfortunately, her lying and betrayal has put you in an even WORSE situation than most. Because every day that child is in your home the closer the two of you become. The child to you - and you to the child. But because you are NOT the biological father - and the man who is has not signed away his parental rights - he could, at ANY time in this child's life choose to assert those rights in court and make your life a misery. This could happen now, 5 years from now or 10 years from now. You are - due to her selfishness and dishonesty - sitting on top of a ticking time bomb that could break your heart and the child's. Even if the other man never chose to assert his parental rights, your wife could leave you in 5 years - and deny you any visitation with the child and might very well be able to get away with it because again, you are not the biological father. I normally try to take a very soft approach with people - but I feel that in this case your situation is so dire, I need to be VERY, VERY direct. 1) You need to see an attorney . Explain the situation with the child and find out if you have ANY rights with respect to the child (I fear you are going to find out they are very, very, very limited.) IMMEDIATELY 2) If your rights are as limited as I fear they are - consider what that means to you, your future and the child's. Because your wife will be able to manipulate your fear of losing that child to make you (and the child) her virtual slave. Any time you don't do EXACTLY what she wants, all she will have to do is threaten to leave and take the child - and you will know that you have no ability (legally) to stop her. Given your wife's behavior with you, I have no reason to believe that she will put the child's needs or attachment to you as its father figure first - and will be quite content to use the child to punish you (with talk of leaving or even doing so.) As the child gets older - it won't just be YOU that gets hurt by this. I have friends who bonded deeply with a step-parent - only to to be ripped from that home when their biological parent decided they didn't want to be married anymore and forbid them to see the ex-step-parent and sadly - the step-parent HAD to abide by the rules or get in trouble with the law! You may NEED to divorce your wife now to protect you and this child from greater heart break at a later date. Again - I could be wrong. Maybe the rules are different in Canada - but you need to get INFORMED by a very reputable and good lawyer asap. I beg you to do so - not just for yourself but for this child. 3) You need to see a different counselor/psychologist. Get a second opinion. I think the advice yours is giving you seems dubious at best. Just like every other profession, not all therapists are created equal. And even if they are good, they may not be qualified to deal with infidelity and lying about paternity. Just like a property lawyer doesn't give advice on criminal cases - counselors have specialties and I have found that there are very few that are REALLY good at handling infidelity. Seek one who SPECIALIZES in infidelity (preferably with some familiarity with your culture and arrange marriages). If they just list it as ONE of a laundry list of issues they work with - they are NOT qualified. 4) Lastly - and I cannot stress this enough - based on everything you have told us, I think there is a strong possibility that your WIFE has a clinical personality disorder (NPD or BPD are both strong contenders.) The other man may very well be too, but I do not believe your wife is some delicate innocent who has a good and pure heart and is being totally manipulated to become a selfish jerk by this guy. The seeds have to be there - he is just watering and nurturing them. I know that many, many arranged marriages work out beautifully. But I fear you got saddled with a bad egg and the longer you try to save it, the more hurt you and this poor child will be when it eventually falls apart after she has mistreated you so long that you finally get the nerve to leave. I really, really, really wish I could tell you what you so clearly want to hear - that there is some magical set of words, or thing you can do that will suddenly make her see the error of her ways and work with you to build a loving and supportive marriage. But there isn't. The only reason she will change is because SHE believes she is wrong and wants to. And she has currently told you that she is not wrong - you are - and the only person who needs to change is you. THAT is what you are signing up to waste your life with. Please don't. You deserve so much more.
BS - Female
Married 27 years, one adult child DD May 2016 “When we are no longer able to change a situation, we are challenged to change ourselves.” - V Frankl