4 kids in those age ranges are going to be madness even under the best circumstances. You can love this woman and have a relationship w/her w/out moving in and being daddy.  Remember that the 4 darlings already have a father and you're not it! If he's a doctor he can afford to pay for their online games and get therapy to deal with their lovely behavior. Your relationship is primarily with your gf not her kids.  

I hope you still have your own place.  

SL is right, everyone is going to need therapy with that mess going on!  When you get involved with someone with children, you get thrown right into the middle of whatever is going on at that point and into the future as well.  We'd all like to think that we'll be seen as what most of us are, a fairly innocent party thrown into the mix.  But, alas!, instead and more than likely, you'll be blamed for whatever they can get away with--much better and easier to blame non-blood than blood.  And, that includes not only the SKs, but bio-dad and even bio-mom, in this case.

Take stock of what you are gaining from this relationship with bio-mom, and decide how you want your future to look.  Stay, go, disengage from the SKs.  You have more options than you might think, but if you stay, you are going to have to turn a blind eye to your SKs' antics and be prepared to have little to do with them as possible, no matter what your GF may desire.  It is not uncommon for bio-parents to, albeit unknowingly, set their partner up for failure with their children and then turn around and act like you are supposed to be their second (if not primary) dad, and then imply that because you are not fulfilling the role as they see it, there is something wrong with YOU.  

You can see such an example already starting with GF here.  I'm not sure what her expectations are for you, but apparently she expects you to stomach her lack of discipline, which, OK, but on the other hand, she could easily at some point in the future go after YOU for not having a better relationship with her children.  Think about it.  Step-parenting is not easy and is very complicated, much moreso than most think.

Your GF needs to parent her kids. Bio dad isn’t the problem in YOUR home, the mother is. (and by the way, doctors work very hard in their education and in their jobs). 

It's only been a year. Cut your losses and get out! These kids will only get worse because no one is parenting them. Even if your GF started parenting today, it's too late for probably all but the youngest.

Nothing is going to change,  If only going to get worst.  Since nothing changing, you have to decide, How you want to live your life ?  Stay, and disengage, or leave.  Or keep your home and just visit 

Dysfunctional families exist across all classes, and some people just never learn how to effectively parent. Your girlfriend is a terrible awful parent and her ex is an absent parent. Together, they've created this mess. 

You sound stressed, angry, and unhappy - and it will only get worse. If you stay, you will lose all love and respect for your GF as you get ground down and become collateral damage.

This woman and her kids are just really, really screwed up. Do you want that toxic ooze to affect your kids? You're attracted to one facet of this woman's personality, but her horrible parenting is also a part of who she is. Sometimes, love is not enough.

Listen, you need to put your foot down on her and her little 'cherubs'. Dont let yourself be manipulated by her either- and she will try her damndest everything from crying, to fighting, sex either by deprivation or inciting it, Even threatening to leave you. This is just how woman work when they are toxic dont pay any of that no kind of mind or phase you. Don't even be angry about it, simply state your terms and inform her of the facts. know for yourself that obviously her way of doing things isnt working for her, its time to try something different. Set your rules and be unwavering. She leaves, so what? You like the kids sure, but they are not yours - and it's better to be single with your hand then in a living hell where someone elses kids dont respect you - plus you gotta pay for it out your money? oh screw that. Your wallet should be completely closed untill you see some changes- and even better when those changes are consistant. 

Until you can get out, double bag it man, double bag it.  Or obstain.  This is a sh!tshow.  Run.  Run fast.

At this point you're just a hamster in a family of pythons

Please explain, to yourself, what makes a person who has raised 4 POS thieving ill behaved crotch trophies so appealing?

I get that she is your Jr High sweet heart but that was 30 years ago.  I would hope that your standards have improved since then.

smh

Take care of  you and leave miss Jr High to her mess of a life.

If you want to stay with this person (also shaking my head), consider that things, as bad as they are now will only get much much worse.

Live separately, and date. If she gets that much money she can afford her own place.

I am assuming she at least pays you rent and food for bratolas? Something? Well, its not worth your peace of mind, and the rug/floor/home wreckers need to be out of your house.

In my particular area, a resort/travel destination/ag biz, I know a VERY LARGE NUMBER of single women, who have their chit together and are very lovely, of all different ages. Im certain I could set you up with someone really nice. LOL. JK, anyways, run far and fast young man. Best advice ever. And free

Cut your loses and get out.  Those step kids will only get worse as they get older because their parents refuse to parent them and insist on spoiling them instead and never hold them accountable. If you do decide to continue the relationship do not move in with her under any circumstances.