in a home invasion most of us would survive without problems A small town punk or a couple of illleagals wanting to stal food and loose items. but in a Shtf sit with troops or Police we wouldnt stand a chance. The only way to prevail in that situation is to not be home when they come to deliver some of their 3 am justice..sorry for the gloom and doom But a shot gun and a pistol is usless against. Mraps and Armoured Hummers with a turrent..
Any small arms that's not AT and is less than .50BMG is useless against an MRAP, HUMMWV are good all they way up to 7.62x51mm.
If troops are rolling, MRAP's are the least of your concerns, they're not like PD's who are rolling in with a handful of barely trained LEO and a single MRAP or M113.
Troops will be reinforcing the armor, not the other way around like you see with a PD. An M2A2, M1126, LAV-III, or LVTP7A1 which will be armed with M2HB .50BMG, Mk.19 40mm AGL, M242 25mm Chaingun, BGM-71 TOW or a mix there of, all of which have FLIR/TIS. This is assuming it's just Mechanized Infantry or Cavalry, not additional Armored units rolling in M1A1/M1A2 which wound be pumping out 120mm M1028 Canister rounds, using their M240 Coax and M2HB .50BMG via CROWS.
Troops are going to be highly trained (most probably veterans), infantry/cav squads, platoons, ect... with assorted small arms, M4/M16A4, M249, M240, M203/M230, AT4, M72 LAW, SMAW, M3 MAAWS, M67 Frag, M32 Milkor MGL, ect... some units will have a DM "Designated Marksman" armed with an M39 EMR or M21 DMR.
Then we're talking specialized munitions like Enhanced Penetrators, Armor Piercing, Enhanced Long Range, Thermobaric, Flechette aka Beehive, 40mm Buckshot, HEDP, ect...
Air Support will be derived from AH-64, AH-1W, MH-60 DAP, UH-1Y VENOM, AC-130, A-10, F16, F15, F22, ect.....
All being supplied intel and logistics by one of the largest military support structures in the world.
They'd send in SOF or SOC assets to deal with the really hairy areas, those that have band together to fight and causing serious problems for regular units, or simply pummel the area into a smoking hole, using serious air delivered munitions.
Having a shotgun, pistol, or rifle isn't going to be the defining point at that crossroads, it's going to be a culmination of skill, ingenuity, and sheer will to fight.