I own a home in AZ but live in FL. I plan to retire there someday. In the meantime my two sons occupy the house. I have a signed rental agreemet but they have failed to pay me to the tune of almost $20,000. I want to evict them... can I do that without spending money on an AZ lawyer and a plane ticket?

You will have to have a agent or someone to evict them.
Have you merely told them to MOVE, and they won't move.

But after they move who is going to clean up the house, who is going to show the house to rent it to someone else.

And unless the rent is 7,000 a month how long have you allowed them to live rent free. ( which is common when you rent to family members) I only rent to family when I can afford to do it for free because family almost never pays.

IF your children will not just move, you will have to go to court to get an eviction, then after the court date they are served and then later they court marshall goes out while you hire someone or do it yourself, and move all of their belongings and set them on the curve.

So if you have to do the eviction, you will need an agent out there are you will have to go out there for a few weeks to get this done