Do about her behavior?  Childten will do what they can get away with. 

I don't think your issue is with your stepchild, it is with your husband.  Does this child have a mother?   

Without her parents imposing rules and punishment, nothing will change.. Since this occurred in Dad's home, he has to be the strong arm of the law. If all he's doing is talking nice to her or pandering to her, she will only get worse. Parents gotta parent and that's on him when it's his house. 

These are attention seeking behaviors. Children don't know the difference and will take whatever attention they can get, good or bad.  At this very young age her perception of the world is extremely limited.  Placing blame on this young child is inappropriate.  Blaming her mother doesn't help any one either.  
 

so... that leaves her dad.  It's his responsibility to discipline and teach his child.  If he's not willing or unable you are in a tough position. Counseling is a wonderful idea, especially if this poor kid is being exposed to drug use. Parenting classes or parenting books can be really helpful.  I practice a lot of positive parenting in my home with my 4 year old.  A bunch of parents swear by the book 123 Magic.  A star reward chart or a daily very small prize from a like a dollar store prize box can also work wonders. 

If this child is in such a poor environment her dad needs to not stop fighting for full custody. Call CPS, get her in therapy and talking.  Sounds like her dad is throwing his hands up which is sad for this girl   On top of both parents sucking she has a step mom who literally hates her   You'd be acting out too. 

The way you speak of your hatred for a 4 year old , a toddler , is disturbing to say the least.  If you want to stay in this relationship you have a vested interest in helping your step daughter/your child's sibling.  I know you are venting but the way you come off makes me think you shouldn't be around this kid either.  She has 2 crap parents, she doesn't need another person around her who despises her.  Kids vibe on these things and it's not fair to her.  You are the adult.  Minimally , I think it's best you disengage until you can manage your outward disdain.  
 

These behaviors will worsen after the new baby arrives.  Acting out at 4 over having a druggie mom and a new sibling is normal.  Lots of one on one time with dad now and especially after baby comes if you can eventually manage. She will highly benefit from one on one positive interactions from you as well. 
 

I hope her dad steps up.  Don't be surprised when he parents your shared child badly. All the counseling , parenting classes , and child development books for you both.  You'll better understand this child and be able to direct your anger towards its rightful owner; her dad.  

Many four year olds lie. My youngest did and did so believably. I once picked him up at preK and they asked if we had somewhere to sleep that night. He had told a story about the house catching on fire and vividly described the firemen putting it out. There was no fire. I was once told that I had neglected to put his food allergies on the form. He had none. They served tuna. He does not like tuna. He told them he was allergic. They stopped believing everything he said. They'd ask truth or story. He grew to be a really good writer of truth and story which is helpful in his profession. 

She's four. I would not label her thief just yet. K teachers spend time each year with lessons on where things belong and why they can't go to your house. It's a lesson a lot of four/five year olds need. 

Your husband needs to step up. He needs to parent this child. And by parent I do not mean punish. Parent is a verb. It is ongoing, not just when misbehavior arises.

You suggest counseling for the four year old. I suggest counseling for all you if this marriage is to survive. 

You expect a 4 year old to think about how "horrible" she is? You and your DH both need to take some parenting classes. No 4 year old should be expected to sit in her room alone and contemplate how "horrible" she is - because she is not "horrible." She is a child who is acting out in inapropriate ways for a reason. And one of those reasons is because she is well aware of your negative feelings towards her.

Oh my. So many thoughts. If you are this angry towards a four year old, you REALLY need to step back and distance yourself. Four year olds can't be thieves, the cognitive reasoning to fully understand what it means to steal something almost certainly isn't there yet. Besides, what was she going to do with money? Can she take herself to the store to buy something? I suppose not.  Give it to her mom? If that's the case, then BM should be the one you're upset with.

I've known a lot of four year olds in my life. They're basically still toddlers. If her behavior is out of control, it's likely that her needs  (physical, mental, or emotional) aren't being met and she is doing whatever she can to get them met. This is very natural and you can't hold a four year old responsible for that. If all of her needs ARE being met and she still has a behavior problem, then it's possible she needs professional intervention. This is her parents' responsibility, not yours. And in case, she probably senses that you hate her and that can certainly impact a child's behavior. You'd be doing her a favor by limiting your interaction.

Chill out - she's 4.  Be honest with yourself as to why you truly dislike her.  You clearly resent her existence - maybe explore that instead of overreacting and generalizing.  Tell your husband you cannot watch or parent her anymore- it would be best for the entire family. 

This child has a lot of problem adults in her life.  She takes things that don't belong to her because she hasn't been taught any better.  Both homes are failing to parent her properly.

All 4 year olds likely lie and take things that don't belong to them.. she probably doesn't even really understand money value and it's not like the kid can walk herself to the local toy store and buy herself stuff.. really.. what is she going to Do withthe money? she isn't so much a thief as a kid who has crap parents if they don't deal with these issues.

OP sounds like she would be better off out of this relationship.. it will not turn out well for her or anyone else in that home based on her attitude towards a kid who is barely out of toddler hood..  IT's too long a road to waste everyone's time.

She is quite young still. At 4 I don't think she even knows the value of money! I think you really need to take a step back and you husband needs to do some actual parenting.

A 4yr old really knows what stealing is. She might be copying something she's seen or just some personal entertainment or hoarding behavior?

When my ss was same age he 'stole' the soap out the bathroom and took it home to show his mum. He also went rifling through my handbag and was about to take something, but again I think it was a trinket for his mum and no idea what was in his mind. I just explained that even if you are allowed to go in mummy's handbag you're not allowed in mine etc.

You do sound really frustrated and fed up but she is only 4, let your husband deal with her and stay out of her way? 

Poor kid. She is surrounded by adults who are failing her. You included.