Assuming Britain defeats the Garda, what next?
Policing Northern Ireland alone had already proved to be a miserable task; occupying the South would be the same experience raised to another order of magnitude.
Any alternatives?
Well first the Gardaí are the police force of the Republic (and being unarmed wouldn't need to be defeated), the Defence Forces are the Armed Forces of the Republic, bit of a difference.
The UK would never have gone South even if the Republic had been insane enough to try this (which as mentioned the chances were very slim), there would have been a punitive action, probably the destruction of the attacking forces, maybe a few strikes at Baldonnel the Air Corps home base, and then economic repercussions ie the collapse of the Irish Economy, probably the restriction of Irish free passage to the UK.