Had a huge fight in front of our little girl

I wasn't there, of course. But getting a big outburst once won't traumatize your child, luckily. You explained it to her and apologized; she only learns from that. This way, she knows it's not normal. Reading this, you seem pretty shocked yourself, so next time you'll probably handle it differently. The most important thing is that you've made up with your husband too. It's not about who was right in that situation, as long as you make it clear that you'll handle things differently next time when you disagree with him. And by the way, even if your husband reacts too slowly to your child, kids also need to learn patience.