How lucky you are, doves make the best pets!
I keep ringneck doves and diamond doves. They are all so sweet and surprisingly intelligent. I used to have white racing homers before that, but had to sell them when I moved to another country.
Any photos of you doves? I am presuming they are ringneck doves?
It takes about 14 days for the eggs to hatch, but some of mine take a day or two longer, so don't throw them away too soon! If you don't want any chicks then you can swap the eggs for any small round white thing. The birds will sit on them and eventually get board and start again.
If your doves are used to you, then you can easily clean out their cage. They are very broody and it takes a lot to frighten them off the nest. Even if they do leave the nest, they will quickly go back. I never know them to abandon the eggs!
The doves need very few things to stay happy and healthy.
1. Dove food
2. Cage bird grit and oyster shell (for digestion and calcium)
3. Fresh water every day
4. Opportunity to bath - can be every day, but at least once a week. (can use a large shallow basin or plant tray , water about 2 or 3 inches deep.)
5. Natural perches from branches of different sizes, (round man made perches are uncomfortable and can cause foot problems).
6. Time to sunbath. You can put the cage outside on a table when you are there to make sure no cats are about. Then need sunlight for vitamins.
I let mine out to fly about in my living room. Make sure the fans are turned off and the windows are closed. Mine are all trained to only rest on their cages or the back of the sofa (with a towel over it to catch poop).
Its easy to train them. When they settle anywhere you don't want them to be, just make them go onto you hand and put then where you want them to sit, or just encourage them to fly off that place (if they are not hand tame). When they land on the proper places leave them alone. They will learn they can rest in peace there.
Some people say their doves like vegetables, but mine don't. I don't add any veg, or vitamins and they are all very healthy and breed well.
Please let me know more about you doves, or ask me some more questions. I am dove crazy! (some of mine can do tricks too).