If you're sick of dealing with them, give notice and terminate, knowing that you will then have to find ANOTHER tenant who may have even worse problems that won't show up for several months...
If you treat this as "business" and simply continue to charge rent and they continue to pay rent, consider giving them the option to actually do the yardwork or to have their rent increased to cover YOUR costs of having it done professionally. Maybe they'd actually prefer having it done nicely by someone else, even though they're paying more rent.
The carpet situation: depends upon how old the carpet is, but many landlords add fees or increase rent for pet owners, knowing that the upkeep and cleaning will be more expensive. It's not "a big deal" if you're planning to replace the carpet soon anyway (i.e., every 5 or 10 years or so), since it will have been fully depreciated, but you can still ask them to pay for "actual damage" to it.
If your policy is that they have no pets it is well within your rights to request them to pay the expense of having the carpet cleaned.
If the value of the property is worth more than you have been charging it would not be unreasonable to raise the rent to what it is worth. However as you surely know, they will not like it. Seeing as the friendship is already on edge that could easily push it to the point of ending. So I guess you really have to decide what you want to do. In the end, the house is owned by you. If they aren't going to respect your wishes in regards to them living there, you're probably better off without them.
You have learned the hard lesson that renting to friends, not enforcing your own rules & being to nice to people does not pay off.
They are destroying your property. You will likely have to sue them for the cost to replace the carpets. There is no cleaning dog pee smell out of carpets! Yes cleaning will make it go away for a period of time but it will always come back. It soaks in to the pad. Given they clearly have no respect for you or your property why on gods green earth would you even consider continuing to rent to these pigs?!
Its time to assert your rights as the property owner and get them out of your property.
I would get them out of the house as quickly as possible. Things are only going to get worse, not better.
The moment you let them move in the friendship was over, so don't worry about that any more, it is history.
Cardinal Rule #1 in Rentals: NEVER rent to Family or Friends. This is the surest way to be taken advantage of. No matter what you do, they will resent you, so get rid of them.
I rent a house to friends on a month to month lease, meaning either side can terminate it with 30 days notice. I kept the rent low and haven't raised it since they moved in (2 yrs ago), and I let them keep multiple pets there (against my policy, but they were friends who needed a place to live).
It's a nice modest house in a very high demand area. I could get another $200 a month easy.
Their dog has been urinating on the carpet. I was over there recently and they brought it up - they were pretty embarrased. Thats a big expense that I didnt expect. They are lazy about outdoor maintenence they are supposed to handle - grass is knee high, flower beds not weeded, no shrubs trimmed. Not too clean inside either, but thats what the cleaning deposit is for. I let them pay rent late a couple times, although I really dont understand why they have any monetary issues since they have good jobs.
Very shortly after I find out about the carpet, one tenant yells at me...multiple times, not a back and forth argument, just yelling. Without basis, seriously. So its clear the friendship is on the rocks.
I gave them notice to take care of the yard within X days. Is it totally dickish to raise the rent? Or should I go further and end the lease?