It ruined my afternoon, that's for sure

We, as a family, had a wretched walk this afternoon. Today marks the second time I tried to walk both my dogs and my kid around the complex. The first time went okay, but not so bad that I would refuse to attempt it again. So this afternoon, I leashed up my dogs, grabbed my toddler, and we headed down the stairs and around the building. The first half of the walk was fine ... really, it was. Sydney kinda listened to me, the dogs are good on their leashes, and the weather was fine. As we made our way towards the homeward stretch of the loop, we came upon the parking lot that must be crossed. I asked for Sydney's hand; "No." I asked again and a third time; "No." I grabbed her forearm, and a screaming fit ensued. I really ignored it, though the more screaming, the more irritated I got. Once we got across the lot though, I let her go to run ahead with the dogs and pick up rocks. She wasn't interested in listening to me, but I knew that we were close to home, so no big worries.
As we came upon the back stairs to our building. the girl living next door to us was coming down the stairs with her two dogs for their walk. The dogs were barking and straining at their leashes, but she held them well, and I pulled Ollie and Daisy toward the walk around the building, avoiding the now-occupied stairs. One dog pulled out of its collar though, and came ran down the stairs toward my pooches. The girl ran down the stairs to get her dog, but that, of course, brought along the second dog. The two dogs then proceeded to swarm over my puppy. They weren't viciously attacking, but it was hardly playing, I thought. Daisy tried to run, but could only go so far on her leash, and then ran back and wrapped her leash around the other girl's legs trying to get away. I reached down to grab her right as she started to really squeal. I picked her up, and then the dogs turned on Oliver. They ran at him, and were basically flanking him. He had nowhere to go and no way to get away. He circled and sat, and at that moment, the girl finally got control of both her dogs and dragged them away. Thankfully, even though she thought she could help, and did get caught up in some of the leash twisting, Sydney stayed out of the direct line of fire.
After all this, of course, Sydney decides to show me more attitude, and demonstrate more of her not-listening state of mind, so I grabbed her and carried both her (screaming and crying) and Daisy (shaking and muddy) upstairs, Oliver (ever calm, though knowing I'm pissed) following closely behind.
It was when I got home that I started shaking and freaking out. I mean, what if, when I had picked up Oliver, the dogs (which were no bigger than Oliver, but had more of an attack pack mentality) went after Sydney? How do you carry all three of your babies in only two arms? I know I would have been able to do it, but the actual fear that strummed through me when I thought of what else could have happened freaked me out.
So, it'll be a while longer before I try this again on my own.