J.D.
S.,
The first priority here is to get you and your husband on the same page in terms of discipline and the parameters for acceptable behavior. If the approach is not consistent for what she does EVERY SINGLE TIME, then her actions won't change. He can't be strict sometimes and not others, and he can't go one way, and then have the rules change when Mom gets home. You two have to be a united front.
Three year olds are tough. They are little individuals, and this is when it's time to figure out just how far their independence can take them. She needs you to rein her in in order to learn what is okay and what isn't. Her behavior within the home will form her expectation for how to treat people outside of the home, so she needs your help to figure out how to interact with strangers, schoolmates, etc. Being lax about disrespect and defiance isn't doing her a service, because the rest of the world won't put up with it, and she'll get totally blindsided by that when she has to deal with other people.
Do you use time-outs with her? That works pretty well, pretty quick with my son, who is 2 1/2. I can tell him a couple of times "NO" and if he doesn't retain that no, a two minute time out gets the message across quick. I rarely have to TO for the same infraction twice. Give her alternatives for releasing negative emotions. She's got to let out anger or frustration somehow, so show her how to do it in a way you consider acceptable. Let her go to her room and jump up and down and yell to "get the angries out". Something like that lets a kid express what they are feeling without being disrespectful or disobedient. I do a lot of "I know that it makes you angry, but you still can't..." And just having someone know how he's feeling helps my little guy a lot.
Best of luck, S., I don't mind admitting three has me shaking in my Mommy boots!