A possibility that I hadn’t considered, though, is that space combat could be pretty brutal (less Star Wars, WW2 naval/Air Force battles, more Submarine warfare where whoever gets spotted first dies). In that case, both sides might want to immediately attack rather than identify themselves as paperclip friends…
With this said, I think that even in this simple objective of paperclip maximization, your war scenario is likelier than eternal peace.
In this case we have a fundamentally straightforward goal, everything must be paperclip. There are lots of steps in between here and paperclip nirvana, but the goal is easy to define and more or less unambiguous. It ought to be possible to communicate a strategy and jointly agree on whether or not it produces more paperclips.
It is possible that the children could be poorly designed, but this seems counter to the idea of the paperclip optimizer. It is supposed to be somehow more competent than humans (after all, it beats us), just following a strange objective.
Why would it be automatically aligned? If for example, the parent AI spawns a child AI probe to travel to a celestial body that doesn't have any metals, in order to achieve some sub-goal, and that child AI would then spawn additional AIs with their own sub-sub-goals, how would the original paperclip maximizer make sure that no such descendant goal ever contradict the generation of paperclips?