I think enough people have told you already that yes, there is a chance, even with a very local two form entry school, that a late application will not get an offer.
A few multiple births, a couple of LAC, a child or two with the school named on their statement, a big cluster of siblings and the number of places available are suddenly reduced as those applications - as well as all the other in time applications - would take preference over your late application.
And sadly being in the Nursery does not count as a criteria any school I know.
Do as others have advised. Keep the original application, you will most likely get a place which means you HAVE a confirmed place for September. When the waiting lists open apply for the preferred school, but of course hang on to the offered place until a new place is confirmed.
For your older child do the in year application. If it is unsuccessful you can make another in year application in September, most authorities only allow one a year. Go on the waiting list for that place.
If your younger child gets a place this might help in an appeal for the older place if that was needed.
If either child gets a place at the preferred school then the others place on the waiting list will improve if they have a sibling criteria.
But the important thing is keep the original application open !!!!!!