As someone who has been a landlord in the past I can sympathize. In my situation I actually had to go to Superior Court to have them evicted it was so bad. They ended up causing significant (>$5K) damage to the premises.
Now in your case the tenant isn't as much of a nightmare, but since the apartment is part of your house they don't have to be an absolute nightmare to cause problems. Making noise late at night being one of them. Let me address your issues as I see them
1. No pet clause. As others have said it doesn't have any teeth. You cannot forbid a tenant to have a legal pet. You're out of luck here.
2. The girlfriend issue. If his girlfriend is basically living with him and you have proof (camera footage is sufficient) you are well within your rights to ask for a bump in the rent to compensate. When you negotiate rental price did that include utilities? I think a better way is to separate the rent from the utilities and have them pay a percentage (for basement usually 1/3 of heat and hydro). That way if a situation like this occurs and utilities rise they are at least paying a portion of the increase. I'd also look into separate meters if possible. The incremental cost of that will more than be recouped when you eventually sell the property.
Feel free to PM me if you have any other questions/concerns.
Now, NONE of what you write is consistent with the provisions of Ontario's rent control system, is it?
in fact, it's nonsense.