Hang in there, girlfriend! Kids are challenging. Speaking as an at home full time mom of two boys who are now 21 and 23, I remember feeling all boxed in, incompetent and angry, and guilty. In retrospect, I wish I'd taken positive reinforcement dog training classes before I had kids! LOL It is amazing how fast a creature can learn good behavior when the right motivation is discovered, a treat, a squeaky toy, or a hug. ( There is actually a series of really good books, called "The Five Love Languages", one for parents, one for women, one for men, etc., that helps us learn how to communicate better to motivate them in a loving way to get loving responses. I highly recommend it!
Sometimes kids (and their parents!) just aren't getting enough exercise, the right food, or enough sleep. And of course, there is always the jealousy factor when vying for attention, and 3 yrs. is the ripest of times for that, because no matter how brilliant we think they are, they are babies in many ways and just don't have the long term capacity to cope well. And, it seemed like the more I yelled, the worse they got, and acted out alot more, too. Vicious cycle, believe me. My husband traveled alot for work too. Even though I had family near by for encouragement and support, I was very hard on myself. A few things I did that helped were talked to the pediatrician about the child to make sure behavior was within what was "reasonable" for a toddler, talked to my personal doctor about my personal feelings/issues and make sure I am not suffering from depression or other issues (I was, plus am ADD and OCD, so never felt good about myself until I got help), and went to family counselor alot to get professional help. Also, have a "positivity" chart for you and your daughter, where you keep track of all the little good things both you and your 3 yr. old do - smiles, sings, shares (whether real or pretend), go five minutes without conflict, etc., so that you get used to catching her (and yourself!) doing the good stuff and rewarded for that, and also you will realize you really aren't yelling all the time. Also, if all else fails, here's a crazy idea that can be fun and refreshing. Take two minutes, go in the bathroom, turn on the fan and water and pretend you are all alone on an island. Splash warm water on your face, then pull out the "good lotion" that smells citrus-y or coconut, and put some on. A little break is sometimes all we need to make us feel better, even if only for a moment, so that we can recover and carry on.
If you really reach the end of your rope and think you are going to lose control, there are anonymous counseling hotlines for desperate parents. I don't know where you live, so I cannot recommend one, but you can probably call your pediatrician's office to find out. If not there, then social services would have it.
Good luck, and remember, someday they will have kids, too! And then you can sit back and laugh!