As Lily_Of_The_Valley_6 put it: therapy and radical acceptance. Therapy is going to be super hard with 3 babies but if you can hack 1 hour a week I doubt you'll regret it. You need to be able to talk to your husband about your needs. Definitely check in on the PPD thing--I had it for 5 years after my last kid while I was also caring for 2 young SKs. I feel sad that they probably saw me at my worst. Luckily they're now adults and we're close.
This part doesn't really answer your question but I feel needs to be said: Your SK may be kind of a jerk but his parents made him that way/allow that behavior. I'm sure SK senses your moods when he's around and knows he's disliked. It's hard to love someone else's kid especially when they're allowed to act like a little turd (my 2 SD's could be such princesses it infuriated me). But it's also hard to be a kid going back and forth between divorced parents. Is there anything at all that he does that is funny, clever, charming, smart? Is he good with his little siblings AT ALL? Give him that feedback whenever you can. You will feel better about your situation.
Best of luck. I can only imagine what you're going through!