Tier 2 ICT Dependant Wife's Delivery is 2 months before Visa expires

[tushantk]

I am in UK on Tier 2 ICT Long term Visa expiring on 27 May 2019, and cannot be extended as per Visa norms. My wife is on Tier 2 ICT Dependant Visa
After the expiry, I am required to serve a mandatory 12 month cool off before re-entering UK. We plan to return to our home country to serve this cool off.

Now the complex situation is

My wife is 6 month pregnant and her expected date is 3 April 2019. Which means, we have around 2 months post the due date until my Tier 2 ICT Visa expires. The midwife told us that we can fly with the baby after 40 days of delivery.

If everything goes fine, normal delivery happens around the due date, and both mother and baby are in good health, then we can fly back before visa expiry without any worries.

However, we want to consider emergency scenarios here. For example, if due date passes by 2 weeks, then 40 days may not be completed by 27 May, which is the day our visa expires. Baby won't be ready to fly by then.

Also, in case of Cesarean section delivery, we have been told there is a checkup after 6 weeks, post which the midwife can allow or refuse travel to the mother.

So our question is, In case by the time our visa expires, mother or the baby are not in a position to travel medically, what can be done in this case?

I heard about Discretionary leave to Remain for exceptional cases, but I don't have enough info on it.

Also, important thing here is that, we plan to come back to UK after 12 months cool off. So, in any case we don't want any kind of Visa ban imposed on our passports due to overstay or breaking Visa norms.

Please suggest , it would be great help

[CR001]

She could of course travel home before the baby is born and deliver in home country.

If your visas expire, you will be overstayers and no entitlement to free NHS or allowed to work or rent.

Pregnancy is not something that happens suddenly, you can make plans and arrangements to avoid such situations.

[poper]

In addition to CR001 comments.
I am not sure what your home country is. In my case, it took a good 3 months for me to obtain my little one's Indian passport as this involves various paper work.
It maybe wise to consider delivering the baby in the home country to avoid all the stress