I'm sorry you have discovered she is cheating on you.
I misunderstood your OP, I thought you were divorced and looking to change residency previously agreed. Now I see that you actually haven't split up with your wife yet.
So it seems what you want to do, is file for divorce, and agree with her that you will be the primary carer for your son? I think you'd be expected to have mediation if she disagrees before any court applications were made.
You're in a strong position to have an equal or greater % of time, as the SAHP. (though it hasn't been 5 years, has it? But 3, and she was the SAHP for 7 years before that)
You will have no more 'right' than her just because she has had an affair. Rightly, the court will be interested in the interests of the child, not in settling a moral score. (I was cheated on, I feel for you - but no court is going to award you residency over her simply because she's moving in with an affair partner)
I don't think it will make any difference to an application to say she has no family support. Most people don't, tbh, and have to manage for themselves. She has a job and can take parental leave or use paid for child care. Many parents have no back up. You don't like this, I'm sorry to be blunt - but she will have her boyfriend for back up.
Arguing for that status quo is very persuasive I would think, but the family support thing I doubt would go far.
I understand why you're trying to get your ducks in a row, but I think you need to start by telling her you know, ending the marriage and actually talking about this.
From your other thread, it seems you both know the marriage is on its last legs.
When I was in that situation with my cheating XH, I threw in some hypothetical questions a few months before I dumped him - including how we would manage child arrangement if we split. Can you sound her out?