The biggest mistake, but very common, is you ignore bad behaviors. Kids are amazing, they pick up on who is strict & who are push overs. Kids need rules & consequences & your kids are NOT to young for rules. They completely understand the difference between good & bad, but they also understand that you don't have rules in place. Good for you for being proactive sooner rather than later.
My son just turned 6, daughter will be 5 & other dghtr just turned 3....some things i do:
back talk or calling names = hot sauce in the mouth
my middle dghtr is my challenge....she cries, hits, back talks, calls names..........its worse when she is tired but i cant get her to take naps anymore so i send her to her room & tell her she needs to find her self control & she can come out when she feels better & stops crying
hitting = timeout (a minute per age), then they have to go to the person they hit & apologize & give them a hug & tell them i love you
Some things you can do is give them a warning & if it happens again then you take away their fav toy or they can't watch tv/movie.......for my kids as it gets closer to dinner (roudiest time of the day for us) I will remind them about the treat they can have if they eat all their dinner but they won't get it if they are doing something naughty. Something else is when you notice things can start to get ugly between them divert their attention to doing something else like coloring, play doh, unloading the dishwasher, etc.
BE CONSISTENT, they will challenge you with the new rules in place but don't give up!