I don't know much about goats, but with most, if not all, animals it's better to leave them with mum - especially if they're feeding. I suspect you'll be out and in checking on mummy goat tonight anyway, so just keep an eye on the wee one and if it's condition changes or it looks distressed make the decision then. But for now, leave them to it.
As for the goat's belly twitching, I'm not sure how long it normally takes between babies in goats, but in pigs if it's any more than about an hour it's a sign that something might be wrong - piglet stuck, wrong way round, stillborn etc - hopefully some of the experienced keepers will be along soon to tell you for sure how to proceed.
HTH
Karen x