It's bound to be harder having to do it all alone. Sounds like you have knocked yourself out to be a great mom. I am really impressed and your kids are darn lucky.

As you acknowledge, your kids are both at tough ages. Mouthiness in a 10 year old is normal, as is the terrible twos. And you don't have that firm dad standing behind you saying, "You heard your mom. Do it!"

They will play you, trying to work in the guilt angle. "Oh, you're such a mean mom. Johnny's mom lets him.....", etc. Don't fall for that. (I know...easier said than done.) Sounds like you are setting boundaries and enforcing penalties, which is good. You might consider boundaries for mouthiness as well. "You know the rules. No more arguing or disrespectful comments. One more word and (no TV for -----, no computer, whatever.)"

You'll probably get some ugly faces, but you know what is inappropriate.

You might consider talking to a counselor about such matters, to get some support and affirmation about what you are doing. It doesn't have to be many sessions. Also, can you afford a babysitter to give yourself a break from time to time? It's called "giving yourself a timeout!"