You'll have to replace the mulch.
I'd try the same sort of enzyme spray as you use in the house. Dollar Tree sells it as do pet stores. Also search "enzyme for dog urine" for other brands. I'd cover the area w/ a burlap sack or trash bag to help along but not smother them.
Try pouring white vinegar on it and hosing it down. Or lemon juice.
white vineyar as above or find a coffee house that grinds their own - supply them with a 5 gallon bucket. Ask them to save the used grounds for you. Pick up the grounds on time that you arrange. This will last and dogs don't care for the smell
I would get a jug of "OdoBan" concentrate at Walmart (I order on line) and put it full strength in a sprayer on your hose and spray it down really good...use enough to soak down into the layers.