Unfortunately that is not the case, the judge must balance the competing harms of action versus inaction to each side, and he must find a likelihood that the parents will ultimately prevail on the merits. that doesn't mean they do ultimately appeal, just that it appears likely at first blush. You can well imagine that a judge can "play" with these concepts as he chooses. I could word a short order ruling either way in about ten minutes each. But there is no way around the requirement for issuing a TRO, it's in the Federal Rules of Civil Procedure which govern the court's issuance of such an order.
"While the statute makes no reference to the traditional equitable concern of "balancing equities," it is a crucial factor in the judge's determination: i.e., the court must exercise its discretion "in favor of the party most likely to be injured . . . If denial of an injunction would result in great harm to the plaintiff, and the defendants would suffer little harm if it were granted, then it is an abuse of discretion to fail to grant the preliminary injunction." [> Robbins v. Sup.Ct. (County of Sacramento) (1985) 38 Cal.3d 199, 205, 211 Cal.Rptr. 398, 401 (emphasis added)]"