The click stand is a great light weight option to hold up the bike but I would have second thoughts about using It in the scenario the OP stated. Loading and unloading a kid trailer will undoubtedly result in the trailer moving the bike forward, backwards , and/or sideways. I would not trust it to reliably stay in place.
it’s a great option for a stand, and one that is easily shared between multiple bikes in your stable, but I would not trust it if I were looking to do what the OP does.