I haven't had this actually come up, but broadly speaking, I would think that the parent would be considered responsible for their new spouse's speech in the first context. It's on them to have a chat with the stepparent and put a stop to it.

As for the second case, that's really too circumstantial, and it might depend on what's being said. "You don't have to do what he says" could have very different meanings depending on whether stepdad is trying to get the kid to sell drugs or trying to enforce a bedtime. In the latter case, I would argue that undermining the stepparent is being used as a means to undermine the other parent's authority. I can't envision Dad (for example) saying "if Mom tells you it's bedtime, you have to listen, but if Stepdad tells you it's bedtime, flip him off."

I will say, however, that something like this is unlikely to be enshrined in a custody agreement, unless the agreement is amended later. An initial custody agreement is part of divorce proceedings (assuming the parents were married, of course). As such, bigamy laws ensure that there isn't a "step-parent" at that time. There may be a boyfriend or girlfriend, but broadly speaking, most custody agreements aren't terribly likely to include people like that, at least not in a custodial capacity. If they're mentioned at all, it's most likely to be in the context of a non-cohabitation clause or similar.