Sounds like you are on the right track. Make sure you praise for every good potty outside, really act excited! My boys are 2 and 3 years old and we still praise like crazy: "WooHoo! Great job! Good boy!"
Clean the accident spots with an enzyme cleaner to remove all scent. Dogs have better noses than we have and may be attracted to return to spot, or the scent may even give them the urge to go.
You are right to limit their freedom so that you can closely supervise until they are fully potty trained.
When they do potty in the house right in front of you, giving a sharp no is okay, but don't act too angry.
Taking them outside often is very good. Also, make sure they go out after every meal, or playtime, or when they first wake up from a nap, or when they are excited. Excitement usually brings on the urge to potty.
Neutering often helps with marking, but doesn't impact good potty habits.
Best wishes to Sammy for a speedy recovery after surgery Thursday.
__________________ Kristin, Max and Teddy |