Cat Aggression?

We inherited an adult pitbull mix 2 months ago from my good friend. We have known her (Sadie) for about 2 years now, and she has always been friendly and incredibly submissive with us. We have been slowly introducing her to our two cats using baby gates and and Sadie's crate, and so far the signs have been great. In the last few days the cats have been getting braver and coming out past the gate when Sadie's laying down, and sniffing her face to face through the gate. Today we were feeding our younger "foodie" cat (Zoe) her favorite special great of turkey, and Sadie obviously wanted to get it, but was sitting and staying obediently. Out of nowhere she bopted past us and chased poor Zoe away from the food. I yelled at her, and am embarrassed to say that I got scared and gave her a hard smack on the rump before pinning her and letting Zoe escape. Afterwards she was incredibly submissive, and when we were taking her to her crate later she completely I ores the cats. The thing that has me scared is that even though She didn't growl or bark, and I didn't see her snap I found a couple of hairs that looked like Zoe's on the tip of her mouth/snout. We checked out Zoe and she's uninjured. I don't know what I should do, are the past 2 months of socialization undone? Do I need to restart with closed doors and sniffing even when I'm home?

Thanks,
Joe