There are plenty of studies that show spanking is not beneficial to children.
I'd recommend that you and your wife take a parenting class, so that the problems with your daughter don't get worse as your daughter becomes a tween and then a teen.
My kids are all different. What worked on one, was actually harmful to another. It destroyed my oldest son, if anyone even raised their voice to him.
But, now that he is a grown man, he is a very kind and caring person.
I think you feel guilty because you know it was the wrong thing to do and I'm not judging you, I did plenty of wrong things.
We also spoiled our youngest daughter and now that she is 18, she has some trouble with responsibility. Looking back, we should have held her accountable more, but I'm glad we didn't spank her.