Why is your wife not mentally fit to remain in the country while pregnant? Is she mentally ill? Suffering depression, severe anxiety, etc.? Or would she just prefer to be at her hometown to deliver?
Delivering twins is risky, especially through IVF, which is expensive, and you and your wife DON'T want to risk a miscarriage, I assume. If your wife is just upset that she can't go home, I'd follow the doctor's advice and avoid travel. Travel causes stress and stress is bad for the mother and babies.
If your wife needs medication for mental illness that is ONLY available in her hometown, then I suppose you should risk the travel, but only if she is very severely ill and threatening to harm herself.
An alternative idea is asking her family to come stay with you until she gives birth. Although perhaps having her whole family uproot and move to another country is asking a lot, maybe just her mother or father, or a sister, or a cousin or someone else she is close to in her family, to make an extended visit to where you're living now would be a fair compromise?
Otherwise, I'd stay put for the health of the babies. Explain to your wife that travel would increase her risk of miscarriage - most mothers would do anything to protect their twins while pregnant, so she should see the logic in this. If one of her family cannot visit long-term, maybe her parents, sisters, aunts, cousins, could visit for short periods of time each, so she'll have family around her at least, even if she's in an unfamiliar place.
Is she worried that being in a different country will affect her children's citizenship/legal rights? In most countries, citizenship is based on where the parents are born - if born in different countries, the child can either choose, or be a dual-citizen (it depends on the laws of the country you're in, and the laws of your native countires, however).
I wish you luck and safe delivery of healthy twin babies!