I think that the real crux of the matter may not be in the "Policing" but in the Internal security bit.

The UK tried to develop an IS paramilitary force with the "Auxiliaries," in Ireland and it was an utter failure as they behaved somewhat worse than the SS. Critical point is that they were Auxiliary Policeman and did not come under military command or discipline (despite being 100% ex-British Officers). Thailand has very screwed up system of "Village Militias" - most of whom are not that good at what they are supposed to do.

Again, the size, shape and doctrine of an IS or "Gendarmerie" is not well researched or written about, but there is ample material to start.

IMO, and IS force should be a subset of the Police, not the Army. They are an enhanced Policing capability, not a military force. They might have a primary role as "Border Guard" - as in Israel.

The real problem is when it comes to "expeditionary IS," which is a pretty good oxymoron!