It is not unintelligible but it is a bit muddled.
OP arranged an in-year admission for DD1, and when this was achieved she enquired about admission for DD2 (then 3). She was mistakenly advised to apply immediately, in May, even though applications would not be accepted until September. She duly completed and submitted a form.
The following spring, not having received an offer, she made multiple calls to the LA who gave conflicting and confusing advice. DD2 was not considered under the usual application round and as the school was oversubscribed she now cannot get a place.
OP, it's a real shame you communicated with the LA only by phone after your initial form. There have obviously been major cockups there (otherwise the school wouldn't have been forced to take an additional 10% on appeal!!) but you will have a real struggle proving that you did everything you could, and everything you were told to.
Go on the waiting list for DD1's school. When is DD2 actually 5? You don't have to send her anywhere until the term after her fifth birthday anyway, I think.
Also bumping so the very knowledgeable will see it.
Good luck.