Why do you have to stay home with the skids? What did he do before you? You shouldn't be giving up all that income for someone else's kids (kids that don't sound like they are very well behaved). ESPECIALLY since you have thoughts of divorce. 

Yes feel I you girl I’m in the same boat and I’ve been married for three years to an enabling disengaged parent bc it’s easier to give in than make the child experience consequences for his poor choices.  I’m the bad cop again right now too and my husband is giving me the silent treatment since weds that’s his go to every time.  I make rules and dish out consequences him and his son are the victims bc I lost it when I couldn’t take it anymore of homeschooling my son and him making little effort to do the work and falling asleep at the computer disrespectful back talk. he’s going to a regular Hs in Jan but the damage my husband has caused of undermining me in front of his son. If a child had no structure or discipline and of course a pat on the back when it’s earned will have a dysfunctional adult life.  Have you tried counseling for yourself.  We were talking divorce after 6 months due to his ways of course I’m not perfect by any means but how much is enough when our fights are on repeat ,  one of my replies to my post was I married beneath me that’s the truth and beyond I feel that way most of the time.  I’m working on my business to be prepared for the possibility of a future divorce and the just in case.  Order of priorities the almighty first yourself and then the children.  Putting your wife last waves the red flags. Do we really listen to them?

me flashbacks:

"the defensiveness sets in and he starts criticizing my adult bios who have never lived with us..."