I think that is the one my friend had. You lift the seat, the adult one stays down, and the toddler one is in the lid, so you use it you just pull it down. It looked very solid because it was porcelain (or whatever loos are made out of) and all built in.
I d want to push Spock, I'm worried she will get an aversion and my pushing too hard will make her scared and fight it....
Great work on your dd1!