Although poorly researched secondary materials published in the 1990s depicted the Missouri State Militia as being some sort of ad hoc organization operating under unclear legal authority, certainly the opposite is true, and there is no ambiguity regarding its formation or its mission. The MSM was formed as a result of direct negotiations in Washington D.C. between Missouri Governor Hamilton Gamble and President Abraham Lincoln in the fall of 1861. These negotiations and the results are well documented, and the day after they reached their agreement, the U.S. War Department issued order formalizing said agreement, which was afterwards followed by an act of Congress sanctioning the agreement.
The primary mission of the MSM was not to support U.S. Volunteers in the state, but to assume primary responsibility for the defense of the state from U.S. Volunteers. With the exception of during Price's Raid late in the war, any U.S Volunteers in the state after the MSM was formed generally supported the MSM, not vice versa. Except for a few detachments of U.S. troops garrisoned in Missouri for just a few weeks here and there, most of which were swiftly moved on to other posts outside of the state after just brief stays there, Missouri was pretty much devoid of U.S. Volunteers for the duration of the war after the MSM was formed (the 17th Illinois Cavalry and the 7th Kansas Cavalry were two exceptions to this rule, and their sojourns in Missouri in the latter part of 1864 were measured in months, not weeks).
The reason for moving primary responsibility of the defense of the state to Gamble and the MSM was two-fold--to free up U.S. troops for service outside of Missouri, and to allow Conservative Unionist Gov. Gamble more direct control of the prosecution of the war within Missouri (the chain of command of the MSM led directly to Gamble, while Gamble was completely outside the chain of command of U.S. Volunteers troops operating in Missouri). And one of the primary motivations for having the defense of the state undertaken by Missourians was to help control abuses against slave-owning loyalists. In fact, by and large, the officers running the MSM were slave-owners themselves (the MSM was essentially operated by Conservative Unionists; compare to Radical Unionists running the Provisional Enrolled Missouri Militia, which led to the PEMM being dismantled by the Conservative Unionists running the state shortly after the PEMM was created.)
As for the mission of the MSM and the authority it had to operate outside of the state, there is nothing ambiguous about that either--it was authorized to operate within the borders of Missouri, "and in the immediate defense of the State." The sanctioning legal authority did not discern between a state in the Union, or a state in the Confederacy. The sanctioning language addressed threats, not politics. The questions about whether the MSM had the authority to make the Illinois raid have baffled me a bit over the years, since the MSM famously operated in Arkansas and Kansas, and I have never seen questions raised about whether the MSM was properly operating in those places.
In any event, if enemy forces were deemed to be operating in Illinois that subjected Missouri to an immediate threat then they were fair game. A ten minute boat ride from Prairie du Rocher, Illinois to Missouri would seem to pose as much of a threat, if not more of a threat, to the state than a 20 hour horse ride from Pocahontas, Ark., into Missouri. And how many times did the MSM hit Pocahontas during the war? Certainly more times than they hit Prairie du Rocher.