J.G.
Lucy O-
The very fact that you feel so guilty speaks volumes. While the action you took was harsh - you love your child. I am in a similar situation as you... a 3.5 girl and 12mo old boy. My daughter is also sensitive and clingy. I think I've learned how to tell when she's working the tears (in order to get what she wants) vs. being really upset. Either way, I'm trying to teach her to cope more effectively with her emotions. If I think she's working it - I get down to her level and tell her that she needs to stop crying (and I guide her through taking some deep breaths to calm down). I then tell her that crying will not get her what she wants - that she and mommy need to be able to talk with one another. And I tell her that sometimes the answer is going to be "no". Of course I'm being overly simple here - but you probably get the idea. The other way to deal with the tears is to have her take a "Positive Time Out" (see positivediscipline.com - founder Dr. Jane Nelson). You and your daughter can set up a "feel better" place in the house - and when she's putting on the tears big time or is really upset, you can give her a hug and ask her to spend time in her special spot until she feels better. (Note - v. hard to use this technique when out and about ...).
I have had some serious lapses in control and judgement since having my second child and have been unduely short tempered with my daughter... the Positive Discipline approach has helped me and my mindset - and ultimately my dealings with my children emmensely.
Good luck.