Whew, lot's going on. I'm going to try and lay out my thoughts here in a semi-coherent manner.
1)The #1 goal is Tain's defeat. The war is paramount. If we lose, it doesn't matter if Jaine has 1, 100 or 0 heirs. Anything that takes away from bringing about victory is dangerous. It is not worth it to sacrific the Circle AND IT'S MISSION, for the life of a child, even if it is the heir. If we lose Jaine, it certainly makes the politics more difficult, but defeat at Tain/Mordred's hands is even worse.
2)My main problem with Archon's stance is the possibility that he's carting around this kid while we're on some longterm mission and that out of our desire to save the innocent kids life, we make choices that are not optimal to achieving our #1 goal: the successful conclusion of the war against Tain.
3) No matter Archon's stance on expectations on whether we "take arrows" for the child...if the child is there, we will take arrows for it...and that can distract us from defeating our foes and that, ultimately, is among the worst things that can happen. It is not fair for Archon to push this unwanted burden on the Circle by fiat. Indeed, if he's so anxious to protect the child, the best option is simply to leave him behind with it, while the rest of the Circle takes care of business. If it comes down to that, Kaereth would rather see that, than worrying about the health and well-being of the child while on a three month jaunt to X to defeat/capture/find out Y.