@Tracey G.,
Where in DE did you buy?
In Delaware, a regular security deposit can only be a maximum of one month's rent, as you said. However, a pet deposit is considered a separate issue altogether. You can either tell them you need an additional month's worth of deposit, a non refundable pet fee, or increased rent (or a combination of the above). They are technically in violation of their current lease, so you can send them a notice to remedy (get rid of cat) or face eviction, or they can agree to a pet addendum with whatever terms you can work out.
If they are smoking only on the patio, but not inside (and are doing a good job of containing it on the patio), you might want to just let it slide. With inherited tenants you can either choose your battles, or evict them and place tenants you screen properly. In my triplex, one apartment contains a group of inherited twenty-somethings that have a cat against their lease, smoke on the patio, and also single-handedly pay all of my holding costs. I'm opting to leave them alone until they move out by choice.
The fruit flies, again, may not be a big enough issue to really crack down on them. It is natural for your feathers to get rustled when you see your tenants not taking care of your new property the way you want them to, but you also have to weigh the amount of damage an issue could cause vs. the amount of effort it will take to remedy said issue. I have never known fruit flies to do much damage on their own, and they aren't hard to get rid of when it comes time to turnover the unit.
My advice would be to get them to sign a pet addendum if you feel that strongly about it, and then coast until the sixty day window before their lease expires. At that point you can either inform them that you are not renewing their lease at all, or you can inform them that you are renewing their lease on the condition that they sign and abide by YOUR lease, rather than whatever lease they are currently on.
Best of luck!!!
