I seriously don't know what you're on iwerta to say such an appalling, incendiary and totally inappropriate thing.
Bananas, I'm a bit confused that you don't understand why you'[re angry. Hello, you have been abandoned, betrayed, replaced; lost your home and, while it is still warm with your presence, he moves in his bit of stuff. All this in your desperate hour of need, when your son is ill with cancer and receiving treatment. And you wonder why you're angry?? 
IIWY I would get a bat and wack the shit out of some cushions with your entire strength to get the TOTALLY JUSTIFIABLE incandescant anger out of your system. imo to hold down such justifiable rage is bad for your health - mental and physical - and you have to get it out. I'm suggesting the bat because it is a safe way to get it out, else you might kill the fucking bastard shit cunt arsehole.
The bat technique is absolutely brilliant for tapping into the rage and letting it out safely - and is followed by a wonderful calm. YOu need it banana, while you go through the process of adjusting to this appalling betrayal. It's not a one-off thing either, do it when the rage starts building up. We british are so off about anger, don't know what to do with it - but it is healthy, an emotion in place for exactly the situation you are facing.
In the old days, women used to make signs/notices, with a picture of the lowlife prick on it, a short description of what he has done, and hang them on every lampost in every street: name him and shame him. If the blog is the equivalent then go ahead, keep it up. I am also of the breed that doesn't believe we shouldn't call a spade a spade: you can tell your lo that daddy has hurt your feelings and you don't feel very friendly towards him at the moment - this, so you don't have to pretend. Imo kids know exactly what is going on but if nobody names it it is confusing for them.
I'm not sure why you lost the house as it is usual that the law supports the woman staying in the family home with the children, but assume there are mitigating factors?
xx hug hug xx