You're completely missing the point, I've got dogs, love dogs, hate idiot owners who let them run up to people, and badly trained dogs who rush up to other dogs.
But the intent of this dog is really crucial here because an excited dog 'wanting to play' (urgh!) and aggressive dog wanting to attack are two completely different things and need to be dealt with differently for OPs safety and for her dogs safety.. neither is acceptable, but it is a fact of being a dog owner unfortunately, it is very rare to have a loose dog attack yours, it will almost always be a badly trained dog pushing it's luck/wanting to play/being a knob.
Rather than taking people's word for it, why not just do a basic google search of what happens when you lift your small dog up when an excitable dog approaches you.. it WILL jump up you, jump around, bark at you, snap even, it's not aggression, it's excitement, your dogs may also go into a state of excitement, fear or aggression, which riles them all up even more, it's all a massive game. OP panicked and didn't know what to do, but she inadvertently escalated the excitement, which resulted in her getting clawed and her having to kick the dog to get rid of it.
If she had stood her ground, and physically blocked the dog, then walked her dogs away the loose dog may have tried to follow but would have lost interest, I've walked my dogs back to the owner before to expedite the process. By staying still OP let the interaction escalate, one of her dogs got hurt by rough play then she picked them up which then caused chaos.
Honestly, this has happened to me hundreds of times, I've had dogs for 30 years and my dog now is reactive of other dogs for exactly the reason above, it pisses me off every time, but I have to do this at least once a week, moving away breaks the focus of the loose dog, especially if it is being called back, and shouting at it / physically blocking it is a secondary option which I rarely have to use. I've never had to hurt an excited dog to get it to go away.