In most areas, especially any that are at all developed, land parcels and minimum lot sizes are under the control of a county or city commission, council, board, etc. Subdividing a property is as expensive and time consuming as you might imagine dealing with the government, you'll probably need a lawyer to do it properly, have to appear before at at least one if not several public meetings or hearings, etc. And they will almost certainly deny any petition along the lines of the examples you offered.

Where I am, things like dividing a 5 acre rural property so that a mother-in-law can live in a cottage near her family are routinely denied.