Which passport control line does my wife (a green card holder) stand in at her home country?

The green card is not a passport. It is a document supportive of passports that allows residency after entering the country and it applies to any country issuing it, especially USA.

She will be using her regular passport, in her case Ukranian, and go through the resident line.

The visa is applicable for the country it was issued for. The passport is the legal document appllicable, as long as it is still valid.

What matters is what country she has a passport with. She would stand in that line.

My husband has dual citizenship and 2 passports, legally.

He often uses his EU passport when traveling alone because the line is usually shorter then the one for US passport holders.

When we travel together we get in the same line and us the foreign visitor line even though I have a EU resident card.

They want to see your passport and don't care all that much about resident cards.

Technically, she's a visitor. The big difference is in the two lines is 1 visas. Which She doesn't need and 2 language. The resident line workers likely only speak Ukrainian and Russian.

I'd either call or e-mail the closest Ukraine embassy or consulate and ask for their recommendation.

Assuming you are flying into Boryispol it depends how busy they are at passport control..My wife is on a Ukrainian passport and i am on a British passport. Usually we just get waived down the Ukraine national channel if it's quiet or if it's really busy