As others have said, if there was a place at the 1st school for a child who lives as close as your DC2 does, you'd have got that even if your DC1 was at a different school. They didn't go for your second because your DC1 is there, you didn't get the first because you were too low down on the list.
The way it works, all the people who have applied for a school (be it as first, second, third) as ranked in order according to the criteria of the school. so imagine if there are 60 places and 100 applicates, 20 of them siblings (no other criteria for this example to keep it easy!), then 1-20 places on the list will be siblings (based off distance within that group), then the rest on distance from school in places 21 - 100. The first 60 of those will be offered a place. However, if some of those top 60 children have actually put that school as their 2nd or 3rd choice and are high enough up the list on their 1st (or 2nd) school list, they'll get an offer on their first school and be removed off this particular school list and everyone else moves up a place, until the top 60 places are filled.
In your case, you weren't high enough up the list on school 1 to get your DC2 in, you would be graded on that list purely off your DC2's own application at that school, regardless of where else you'd put on your other 3 options. With the sibling link, you are therefore high enough up on the list for school 2, but if you'd got school 1, you'd just disappear off the list for school 2.
Appealing isn't like asking again, you have to say they applied the criteria wrong, and it doesn't sound like they did. Your DC2 doesn't have a sibling at school1, so is just judged like an only child/a child without a sibling in primary school, purely off distance, and this year you live too far away.
If you are very close to school 1 and think you have only just missed out on distance (which it sounds like if DC1 would have got a place when he went), then go on the wait list, other people will move about, some will go private and turn down places, some will go on wait lists for other schools and drop off your preferred school list.