Be careful with the lawn hose, that core normally operates at ~18PSI, your house pressure can be like 50PSI so don't blow up the core.
Use the hose in a forward backwards motion, flush the top then move the nozzle to the bottom and reverse it, keep doing that till it stops blowing chunks of crud out.
Also drain the system, refill with water and add a bottle of the Prestone 7 hour flush and then go drive it for the time specified. That stuff does quite a job.
Better do it soon before temps go down to freezing and using water and flush causes problems. If you have never done it would also suggest replacing the thermostat and the pressure cap, get them both from the dealer.
The heater core replacement is at least a 7 hour job, the dash has to come out.
If you go that route and have A/C I would also replace the A/C's evaporator while you have it all apart. Evap failure is common on jeeps.