Well for one he's probably going through alot with feelings of being left out, because I'm sure he knows ppl do not want him there if he's bad. Also he could have adhd or some other form of mental illness so a psychologist should be looked into. If I were you I would try to act like he was your child , because he is a child , and love him and be patient with him. Give it time and try giving him respect so he will respect you. Good luck.
I know this much, children these days have it so easy! One major thing his mom is doing wrong is saying no baseball then taking him, he knows she is a push over! Now I bet she makes him miss baseball a few times which means sticking to it this little man's attitude would be completely different towards her.. because right now he knows she will say it and then just say to hell with it and give in.. at 12 that's not a great thing to do, my guess is he knows without a doubt he can act however he wants and she doesn't mean a single word she says for discipline! Now imagine this at 14-15 years old when he is possibly making terrible choices like many teens do and him knowing its good mom will bail me out of it! I know his mom is not doing these things to harm him, but giving in is actually harming him... because at 12 he knows without a doubt right from wrong!!! Again, you stated he is already a follower his mom and you have to do something now..
I know many states have scared straight programs but the mom would have to be on board with it which could be a tough one. So, perhaps maybe a psychiatry visit is best, he may have adhd.. I have adhd and never outgrew it and I'll be honest my mouth and attiude at times can be way out of my own control, and after I've calmed down I'm left with heaps of apologizing to do.. maybe both you and mom try to sit with him and set up chores he might be a little bit more on ball with? So that way he feels he has some say in it, which may help tremendously! The cleaning his room one is a no brainer, it's his own spot and he makes the messes. Vacuuming maybe narrow it down to his room and the hall that leads to his room? Laundry, well that's a tough one because I am an adult and hate laundry, but maybe work on him with it so it doesn't feel so overwhelming? Like help sort it, and such. Not saying do the entire chore with him but help him with the sorting and getting it to the washer? Again, this is only advice. Most important is the mom has to say what she means and means what she says, caving in isn't helping him, its hurting him now and in the long run!
Trust me I am trying to teach my sister and her husband this who'se four year old has a mouth like a trucker and is still on a bottle and yes he has sensory disorder but it's also them saying no toy because you called dad a piece of sh** and the dad literally handing him the toy because he cries!! Mixed messages hurt kids now and in the long run...
At the end of it all, when hr turns 18 its the parents who are supposed to teach right from wrong, structure and build a child into a somewhat functioning adult. Which these days is so difficult, it "seems" like you put a child into time out it and it's child abuse, every bit of a parents rights is being robbed away from them... then when the child breaks the law the judge is looking at you like where were you in this child's life? Oh I couldn't parent because parenting these days is against the law.. smh, sad times we live in!
He certainly has many, many symptoms of ADHD - probably the inattentive type - which would explain a lot. Check out this link - https://www.helpguide.org/articles/add-adhd/attention-deficit-disorder-adhd-in-children.htm
If you have questions or need more info please post here or on the ADHD site where I am also the CL - http://www.medhelp.org/forums/ADD---ADHD/show/175