I am Presuming your enquiry is for next year in main Summer holiday period. Regarding the passport issue, all airlines now require photographic ID, passport being the obvious but citizens card or driving licence also acceptable with most airlines. Jersey has all the major banks but if you have a building society account then you may have a problem. Regarding when to visit and where to stay, the weather is very much the same as the South West of England but can be a couple of degrees warmer. You do not state what you budget might be but one of the best hotels for children is the Merton Hotel
as they have so many facilities, including their own aquadome and flowrider, so even if the weather is not ideal there is always something to do. They also have single parent deals but early booking is recommended. If however you prefer something near the beach I would suggest the Miramar (above Saint Brelades Bay) or the Golden Sands Hotel
(on the beachfront at Saint Brelades Bay).