Our K1 application is being sent to the embassy, and I hope our appointment will be scheduled soon.

I was wondering how hard it will be for us to visit Ukraine after our marriage. I understand the rest of the process will take a couple of years.

After moving here, Laiza wants to visit Ukraine in May. Would that be possible?

Unless Adjustment of Status has been completed and she has received her conditional green card, she will not be able to leave the country. You must file for advanced parole when you apply for AOS; if granted, this will give her permission to leave while her AOS is still pending.

Definately apply for advanced parole when you apply for the AOS. If she leaves the country without that (or her conditional greencard) she won't be allowed re-entry into the US, they'll consider it as if she abandoned the visa.

As far as what I have understood it make take up to 2 year, beforeyou are actually allowed to leave the US after enetering on a K-1 visa.
You'll have serious problems getting back into the US after coming back. In special occasion, like serious family issues you need to get permission.

Read the "Working & Traveling prior to getting a Green Card" forum here. That will give you a lot of information.

When you apply for your AOS, also apply for AP at the same time. It takes about 2-3 months on average to be approved for AP.

AP is not just for serious family issues. Normally APs take about 60 -90 days to be approved and can be filed with or after AOS application. If serious issues arise, the AP can sometimes be approved faster at the discretion of the district office.