I prefer "from" with "different", but I'm not sure that "than" is the the main problem. That whole construction, whilst quite common these days, seems awkward to me. "Different" is usually about a comparison. That sentence compares children with an exit, which doesn't make much sense. You'd have to re-write it completely:
It means that all children travelling home on a bus and those walking home have to leave by different exits.
It means that all children travelling home on a bus have to leave by an exit different from that used by those who walk home.
Re-ordering the "different" to be next to "from" flows better (IMHO) because "different from" is describing the exit. I've removed "all" because the whole sense is that the transport home determines the exit, so that would naturally apply to all the children concerned.