Re-reading through this thread several things strike me- nothing to solve this mystery but some puzzling things to consider.
1) So far, I think, the only place which gives Annie's maiden name as McKinstry seems to be her son's marriage record. So, that could be misleading if not her maiden name.
2) If Annie was married to a police constable then to apply for a pension after his death she would likely have to have submitted paperwork to substantiate the claim (marriage record, birth or baptism records for the underage children)
3) I think that RIC men were not stationed in their home county or that of their wife. John McCabe was born in County Monaghan then stationed, mostly, in Belfast according to report of his death. Would be interesting to know where he was stationed before Belfast. However, 1911 census Annie says she was born in Coutny Antrim and children in Belfast.