It really is horrible to see the decision in writing and I sympathise.
Is the school the children currently attend the nearest one with places and is it more than three miles from their current home?
If yes to both, they are eligible for school transport and the LA has a statutory duty to provide it, whatever somebody on the end of a phone has told you.
Your next step should be to apply formally for transport. You can usually download the form from the council's website. You might need to include a covering letter explaining that you have been turned down by nearer schools. The unsuccessful appeal will strengthen your case.
If the LA refuses to provide transport, you must then appeal and then refer to the LGO. The sooner you start the process, the better.
Your DDiL must also decide quickly what to do about the eldest child's secondary education. If there is no realistic chance of a place in the preferred secondary school, you have two options:
a) Apply anyway and keep your fingers crossed, but have a second choice which would be acceptable. Bear in mind that if you don't put the second choice first, it might also be full with those from the top of the list and your grandchild runs the risk of being allocated another school.
b) Put the second choice at the top of the list and be almost guaranteed a place.
PS. You're right about the decision being made before the appeal. The only thing that matters in appeals is the law. The school had a strong case, because it was full. Your only case would have been an argument that the school would have provided something no other school could. The appeal would not have taken into account any transport difficulties or any other emotional appeal. The only way a transport problem can succeed is if the child is disabled (and, therefore, can't walk or travel long distances) or if the school is hours away from the home, for example in a very rural area, in which case it becomes unreasonable for the child to travel.
There was almost nothing you could have done, so don't feel badly about it. Very few appeals succeed. You might find a visit to the CAB helpful.