Between Bio-parents and Step-parents. Between the children of both. Between the rest of the family.
Most people I talk with say they most argue about money and kids. I would agree. Differences in parenting styles, in interpretation... one parent 'catching' what the child is doing while the other parent thinks it's 'nothing'. The child sensing weakness and exploiting it unconsciously (or consciously) just to see where the boundaries lie.
Here's an example of how tangled things can get.
DH had a hard evening home with DD. When I came home, DD was in trouble, DH said 'I don't want to talk about it, let's talk about it tomorrow'. Since I was tired and DD was already in bed, I agreed.
Tomorrow came. I picked DD up from school and we came home. She asked to go do homework with a friend. I said ok, but be back by 5pm. DH came home just as she was leaving and asked where she was going. He then told me that her punishment from the day prior was not to go to her friend's house. She agreed that she had made that agreement with him.
As BM, I overrode DH's authority. Here's why: I told DD that because DH and I had not communicated, and I had told DD she could go, that she could still go. But I told her that I did realize she tried to go around DH, and that doesn't work. So, her punishment of not going to the friend's house still stood, but the length of time would start that day, instead of the day prior. Still the same punishment.
DH agreed with that (albeit reluctantly).
DD went to her friends house. Later, I was walking down the driveway and saw them in the trees doing their work. I said hello and asked DD how her homework was coming. She said she had two rhyming pairs. I asked what she had. She said something like "surprise/dedise". I asked her what "dedise" meant. She said her teacher said she could make them up. I told her that even if that were true, I say she needs to use actual words. Goodness knows there are plenty to choose from.
She threw herself down and made disagreeable noises. DH came up behind me and said, "that's it, that's what we were talking about, it's time for you to go home".
When we got back to the house he explained that her attitude was so bad after leaving that girls house the other day that he told DD that until her attitude improved, consistently, that she couldn't go play there. (and I totally agree, this little girl talks to her parents horribly and is in general a little brat, IMO). As DH said, this is a good lesson for not letting the attitudes of other people/friends influence your behavior.
DD started yelling from her room "mom, I love you mom".
I walked back there. DH tried to stop me because he didn't know what I was doing.
I told DD that she made an agreement, then she tried to pit me against DH. I upheld my agreement with her, but the punishment still stood. Then after I went against DH's original punishment (usurped his authority as SF) she engaged in exactly the same behavior that got her in trouble in the first place. I love you, but this style of interaction is not acceptable. So don't call out "I love you mom" thinking I'm going to rescue you. You did this to yourself.
DH thanked me for backing him up. I apologized for going over him. He apologized for not making the punishment clear to me (because really, that's what started the whole thing).
All in all it took up the better part of two hours and a lot of diplomacy.
And we both realized that even after five years it is still so difficult to balance what we think is right with the kids against what the other adult thinks is right with the kids. And presenting a united front is really hard, especially if you don't agree with what the other person is saying.