A.,
I'm sure this is very difficult for you. Here is my advice:
Your daughter is used to getting what she wants. She's been getting it for 3 years. What she's not used to is having Mom say "No". So, she's going to have to get used to it. If crying and throwing a fit gets her what she wants (or has in the past), she will continue to do that until she gets what she wants. You have to teach her that throwing that fit DOES NOT get her what she wants any longer. So, what do you do when she starts throwing a fit? Leave the place where you are at. Simply scoop her up kicking and screaming and take her to the car, put her in, and go home. No candy, no outing, no fun. Simple as that. I realize that it's not always easy to leave a full cart at the grocery store in the middle of an aisle and leave b/c you have a screaming child, but we do it all the time. Also, if you are in a place where you can't leave (maybe you are just getting ready to check out at the grocery store) and she is throwing a fit, just ignore her. Trust me, anyone is a Mom around you will understand. If anyone says anything about her fit, just smile and say it's the "terrible threes", or "she's not happy that we're not going to eat candy for dinner". If they don't understand, they don't need to. Don't worry about her tantrums. She's doing it to try to get attention and to get what she wants. If she doesn't get either, she'll realize that tantrums are just a really big waste of energy.
As for the buying her things out of guilt, you are only playing into this behavior of hers. You need to stop buying her stuff out of guilt. Your daughter needs your love, attention, and guidance, not something that you purchsed with your credit card. Those extra toys aren't going to buy her love or acceptance. I understand your guilt, but it's not the right way to handle the situation. I'm sure you are a great Mom and you spend every minute that you can with your daughter. That's enough!! That's all you need to do. Love her and protect her and raise her with good values and you've done your job. If you continue to spoil her with things, the situation will never change, and she'll grow up with a sense of entitlement and also to understand that people show their love for her by buying her stuff. Do you really want her to think that a man is supposed to buy her stuff to show her that he loves her? Compensating for her lack of a father is not something that you can do. Facts are facts. Her father has chosen not to be around (his loss!)and you shouldn't feel the need to fill that void. You are all that you daughter needs. I was raised in a single parent household and I'm fine! I'm sure you know plenty of other people who were raised by single parents and they are just fine too. By doing what you are doing, and trying to "fill that void", you are already fostering a sense that she is "damaged" by not having a father around. If you don't make it out to be a big deal, she won't ever think it's a big deal.
Good Luck!!!!