I am just going to throw out some ideas, as I have never rented with a roommate. I would say to make life difficult for her and him, without them thinking you are doing it on purpose. You say that you can afford the place without her, so try this. It may be difficult, but stop buying groceries for awhile and take your children out to eat. Hide extra toilet paper, toiletries, anything you can, so that they run out of things to use and have to buy their own. Then start eating their food, using their toiletries, etc. If they complain, tell them that you have spent too much money in utilities, food, etc to afford to restock and tell them that they will need to kick in for a few weeks. Maybe it will finally occur to them that they would be better off getting their own place. Don't be aggressively difficult, just don't make it easy for them to stay there. It would be great if it was their idea to move out.
If this fails, you will probably have no choice but to talk to your landlord to see what he may be able to do, if anything. Ask him not to talk to them about it, or his property may get damaged, if they get angry with her, since she paid the security deposit. You could also just come out and tell the landlord about your roommate breaking the lease terms by bringing in another person and a dog, and see if maybe she will post a 14 day termination notice, letting her know that he and the dog is in violation of the lease and she and them need to move. She will probably know that you reported her, unless you arrange with the landlord to stop by at a certain time, invite her in,and let her see what is going on (although your roommate will probably just say that he is just visiting).
You could also just talk to her, one on one, and tell her that this is not working out and you would like for them to find another place. She will probably refuse to go, but you never know. She may be thinking the same thing, although with a loser boyfriend with no job, she probably knows that she can't afford it on her own.
I hope this helps. I really don't know what else to suggest.