Your DH gets mad at you because you do not want to be hit by a child?  You have got to be kidding.  Wow, I thought mine was enabling!  You might want to mention to him that one day soon she will be in school with other kids and she is goiing to hit the wrong one.  One who is going to punch her "lovely" little face in.  If he doesn't want that to happen he had better take her to a shrink and get it under control.  If the problem is the mother's influence, possibly her disciplining the child with violence so that she is learning the lesson that violence is the right way to solve problems, then a custody modification filing following the shrink's evaluation may be appropriate.  There is time to turn this girl around but at 5 and a half she is quickly forming the basis of her personality.

At 5 years old she is hitting people like that?! That is insane.... and I would say not normal.

i would tell her that hitting is against the law and if she hits you again or someone else that you will have to call the police to come.  My ex had a daughter who was about 5-6 and would hit him (she wouldn’t dare hit me) but when I told her that it was the last time she hit anyone. 

OK, this is the hard and unvarnished truth. You are the other woman. His wife (they are still married) no matter how abusive she was and no matter how unbalanced she is - she has a right to feel angry about the betrayal.

Now, I get this. I have had an affair, too. More pertinent, my SO was in a situation like this. He was married to a verbally and emotionally abusive woman - he suspects BPD and I tend to agree based on the experiences I've had with her. She is emotionally abusive to the kids. He had every right to leave. In his own mind he left of his own accord, but the reality was he ended up with a woman he was having an affair with (not me). BM was angry. Super angry. He still (stupidly) thinks that she doesn't know for sure that he was having an affair, but BM is not an idiot (like yours has many good qualities - including intelligence). She knew, she just couldn't PROVE. What she has failed to realise is that her behaviour is what really drove him away, because the other woman was also married and they did not actually get together officially for another year. The other woman was a catalyst and not THE reason. But BM will never realise this because it would mean acknowledging her own behaviour. She never was able to accept SO's new GF and continued in anger for their entire relationship. It's not plain sailing with me either, but I have the advantage that I am not the other woman in their divorce. That woman was a constant reminder of what she felt was an unforgivable betrayal and that may well be you. 

BM had children about your SD's age. She involved them in emotional matters well beyond their years. It was turbulent and awful and it was no doubt difficult for them to process this. If the BM in your life is unable to handle her own emotions - she will not be able to protect her daughter and in fact will be exposing her to more turbulence. She has a right to be angry and people who are already unbalanced emotionally are not able to handle that anger in a mature way and the backlash hits their kids even if they don't want it to. 

SD is angry. She has a right to be. Her home life has been broken up and after only 5 months or so daddy wants to get some stranger to co-parent her. She is only little so can't handle her anger. She doesn't have a good model of handling anger from BM. It's no wonder she reacts this way. 

This is not a case of discipline alone. This is a case of helping her to handle her anger in better ways. But this is a case of discipline in terms of dealing with outbursts of violence which is never acceptable.

Whatever you do - DO NOT HIT BACK. SD needs a model of handling anger that is better. But also you could be in serious legal jeopardy.

Unfortunately, I also see red flags in your SO's behaviour. This 'poor me you don't want me to love my daughter' business is dangerous and a form of emotional manipulation. Sorting that kid out is going to be hard work and require patience, he doesn't seem to want to do that. Perhaps that's why he's pushing co-parenting so hard. Your job - at most - right now is to support him in parenting. It is NOT YOUR PLACE to parent this kid - yet.  And frankly, your relationship has everything stacked against it - if you care about this kid, keep a bit of distance, because the likelihood is that you will be another loss, too. So give it time before you go in with hands-on parenting. 

I've been with my step kids for over a year and I'm only now really 'parenting' them and disciplining them. And I have a bio son their same age so it's not like I've not been actively parenting in front of them. 

Welcome to the site! Your partner needs to address this seriously abnormal behaviour of hitting, NOW, and stop putting the ball in your court.  I wouldn't hit back, but I would physically restrain a child that was hitting me or another, or threatening to hit, and I would put the child in a "time out" in its room.   

I don't know what age children start school where you are, but where I live in the UK it is usually around 4.5 yrs.  No teacher is going to put up with a child that constantly hits others, so it is likely the child will be excluded from mainstream school.  

Honestly, I suggest a come to Jesus meeting with your partner and find out how he proposes to address this, right away.  

Wait I'm confused, he's going through a divorce yet is re-married to you? How did he get around the system to do that?

Hmm so a child who hits you and a husband who gets angry at you because his child is hitting you, oh and he's a cheater to boot, please tell me what redeeming qualities (aside from good teeth) this man has?

Welcome to ST

I see by your bio that you have been with us for a few hours. 

There may be serious reasons your husbands child hits family plus YOU. A child Psychologist should be able to get to the bottom on it. Could be mental health issues and if that is true the school would have told DH his child is hitting other students AND staff. You would already know about that.

Problem is BM has not told her daughter MOMMY and DADDY love you. Mommy and daddy are not married anymore.  When you go to daddy you must never hit anyone. If you are sad or mad you must use your words.  Daddy wife is NICE and you will have fun with her. BE a good girl and never hurt anyone ok?

MOM is failing her kid...and dad, well being mad at you is not his best moment. GET that kid in to a Dr of child Psychology. Nothing less than those credentials will be epic failure.

Keep it simple.  Set the standards of reasonable behavior in your home and enforce those  standards with escalating unpleasant age appropriate consequences.

Both of you enforce them.  If he doesn’t like how you parent and discipline then he can step up and get it done before you have to or STFU and have your back.

This requires a foundation of the two of you being equity life partners and equity parents to any spawn in your household regardless of spawn biology.

Or in shorter words.... someone put this toxic crotch nugget over their knee and light her ass up.

Lather, rinse, repeat.

No one applied effective consequences to BM’s backside when she was a violent toxic crotch dropping and look at that outcome.  This kid is a product of that same shallow and polluted gene pool.  To rescue this kid from the shallow and polluted half of her gene pool will take dedicated consistent effective enforcement of behavioral standards and application of escalating consequences.

Seeing her violent BM frog marched to the back of a police car in handcuffs would set the right tone for the life time effort this is going to take.