It sounds like you're in a cycle of power struggles - those can be tough to handle, especially with a 3-year-old. Especially a 3 y.o. who's probably missing her daddy and doesn't understand it all.
I also think Pam made some excellent points, and while I agree that her book suggestion is an excellent resource, it's geared for parents of older children. For a 3 year old, I would HIGHLY recommend Positive Discipline for Preschoolers, by Jane Nelson.
Nelson's methods will teach you how to be both firm and kind at the same time, and most importantly, how to avoid power struggles. My older son's school (Pre-K to 8th grade) uses the Positive Discipline model as it's comprehensive system of discipline for the entire school - every teacher gets training in it, every parent is instructed to read the book, they have frequent workshops, etc.
Time outs aren't good for dealing with tantrums, although it's better than hitting (popping or spanking) or taking off doors. (Of course, the same argument could be made that hitting a young child is better than shooting them -- but that's hardly a ringing endorsement for hitting.) If a child is REALLY having a meltdown, they aren't in control of their emotions. You have to get them past the drama, back in control of their emotions before you can hope to reason with them and get them to understand what you're trying to correct.
How many children, when ordered in to a timeout, even when instructed to "think about what they did wrong" REALLY think about what they did wrong? There's no great enlightenment that's occurring, just stewing in anger, or worse, plotting revenge. Seriously think about it, imagine yourself in her shoes. Have your husband pretend you are the child and order you into a timeout - or even just look in the mirror and do it, with the same tone of voice and scowling expression. Does it make you want to be a better person?
You don't HAVE to make a child feel bad in order for them to do behave well. In fact, while the fear of punishment will buy you some short-term obedience, in the long-term it WILL set you back. It's not teaching kids to be kind to others, to act ethically or fairly or do what's right. It's teaching them to watch out for their own behinds and that it's OK to hit people smaller than you, even if you love them. Ouch!
And children who are hit tend to hit other kids. My kids play with a 6 year old boy who gets spanked by his mother, so the kid thinks it's an appropriate way to correct a younger child. So my 3 year was playing with him and did something wrong, knocked down some blocks or something, I don't even know if it was on purpose or not, and the next thing I know, this 6 y.o. kid has MY 3 year old over his knee and he's spanking him shouting "No! BAD!" And what does this boys' mother do when SHE hears about this? She REALLY wailed on his backside then and grounded him for weeks on top of it! Seriously! Talk about a mixed message! We can do better than this, folks.
Good luck!