I'm not sure about the safety of the plastic she's using, either. My rule is that caustics are in known-safe plastic types, or stainless steel.
The lack of gloves thing...guilty. I'm too clumsy in gloves, and I'm not exactly graceful without them.
However, remove all rings and bracelets. They can catch, get raw soap under them or, in some cases depending on what they're made of, chemically react. That's Safety 101. Ask me how I know that...
However, that bloody pinkie with the scarring? Bandage, please, or you're going to chemically debride that thing. Not to mention the ew factor of having a wound open near soap you're making (although what with lye, that's not exactly a major issue).
I fold in my scent rather than stick blending , which isn't a safety issue, but helps protect you from an accelerating FO or EO.
Get the kid out of the soaping area. You're the adult, he/she is not responsible enough to be around raw soap.
Never, never, never pour or scrape towards you. A slip will send caustic raw soap down the front of you, a flip with the spatula can send it into your face. Always pour to the side or away. That's a good rule for hot items, as well. Ask me how I know that...
Do NOT allow children to play with balls that can fly up and knock over your new, still-caustic soap. In addition to not having the kid in the soaping area as mentioned above, of course.
In general, she moves that mold way too much; every move is a potential spill. Once placed, my mold does not move. I move around the mold.