the risk is huge.
You will need to have the flights (and accommodation???) booked well in advance, especially because it is Easter (I presume you can book a flight for an as yet unborn baby?? I know they won't need a seat, but still need mentioning on the booking!) , then the passport logistics are hugely risky and the time thing again made worse because of the Easter rush.
Daily, I am glad if it all worked out for you, but even as someone who took my 9 week old abroad, I wouldn't not have anyone 'insist' that I take a newborn to India (injections?), long haul flight, and start formula just to facilitate a 'destination wedding'.
If you can't travel, either because of an overdue date CS, or passport complications (first passports always take longer than renewals), or what ever, then you will lose the lot.
Your sister took a big risk when she booked her wedding for Italy at Easter if she feels strongly that you go. If she really wanted the twins as page boys she should have thought bout the practicalities.
IT may well cause a massive row if you don't go - cause a massive row if they try and make you against your will!
Sorry, I know this doesn't help when you are depressed, but it really is them, not you. That might give you some comfort.