Postdoc project: Bait and switch
You have been scammed. I recently went through a rather similar situation, see the thread below:
Persistent issues with salary pay as a postdoc in China: What can I do?
Apparently there are several cheaters fishing for foreign postdocs into such schemes. Tracing the parallel of my situation onto yours, I was hired by a Chinese university on a false salary expectation under their pretence that all my project ideas sounded interesting. They were keen in that I would convince my wife to move as well to another department, and kept encouraging us into joining the university later as professors. As soon as I landed and lodged, salary was "unexpectedly" irregular and much lower, and they started pushing to work 12/6 on other undiscussed projects. Their strategy of manipulation was exactly as you describe: no email communication unless where I complied with their demands.
I played their game until the end of the contract. I am sure they hoped I'd give up. I was actually benefitting from investing time on personal projects, saving money, and learning a foreign culture while they shunned me. I kept wondering whether they'd eventually kick me out, which they never did. But I do not recommend this line of action: I do not like playing games, and everyday I felt angry. Furthermore it is a waste of time, in the end.
My advice to you is that you focus 100% on networking and finding another job asap. Apply for an industry position within the same region. Of course the PI will feel you're up to something but try to keep this person isolating you. (A trick is to look miserable whenever you're seen.) They expect you to just settle, and they probably will not fire you unless given a good reason. So don't fall for any provocation, play victim, and invest heavy on getting a new position. How is your LinkedIn profile? Ever heard of The Cheeky Scientists Association? Aware of any networking fairs around your location? There is a lot to be done.
You will win: just bite the bullet and cheat these cheaters. Good luck.
That's a really annoying situation!
I'd start by seriously considering finding another postdoc position somewhere. It may not be possible due to the job market and because of your spouse and kids, but you need to find out if this is a possibility at all or whether it is not. Talk to your spouse about this and put out feelers for other postdoc positions.
If that doesn't work, look for other work in or around the city you are living in right now. This would mean leaving academics and that's a hard pill to swallow for some, but many, many people are perfectly happy not being in academics.
The final option is to find a way to make things work in your current position. I'm ranking this third because you sound like you lost trust in your supervisor and/or employer and that's quite difficult to recover from.
Good luck!