UK Tier 2 ICT Visa Expiry and expecting anytime now

[Muthappa]

Hi there,

I hope someone can shed some light here with regard to a complex situation i am right now.

I am currently working in the UK on Tier 2 ICT long term visa. Due to 5 years stay limitation in last 6 years rule (came to know now), that my company can not extend it and I just have exactly 2 more months left in current ICT Tier2 visa. My wife is pregnant and expecting anytime now as am writing this on the due date provide by Mid wife.
Requests to provide a different CoS or PBS has been rejected (this is when you get to know what company can provide you when in need)

So as they are pushing me to offshore, getting the birth certificate, an Indian passport and visa (do we need one) for my kid would be challenging- any rough estimate how long does it take ? And what would happen if it gets delayed? I don't want to be overstayed.

Kindly suggest me if there are any other steps i should take or do you feel everything will be fine by the time I have.

Regards,
Muthappa

[Muthappa]

@mods - Appreciate your insights on this please.