Oh dear!
Ease (or otherwise) of journey to school is simply not a factor in school allocations. If is all down to how well you fit the published entrance critera for the school, and it sounds as if you were simply not close enough to your preferred schools.
You need to check the rejections carefully, to make sure there is no administrative mistake (putting your DC in the wrong category, or getting your address, and therefore distance to the school, wrong).
Assuming no error, you need to make sure your DC is on the waiting list for your preferred school and add him to the lists of any which would be easier than the currently allocated one.
You can apply for schools in other council areas, but the oversubscription criteria is likely to be distance from the school. So unless your parents live near an undersubscribed school, you need to be realistic about your chances of getting a place so far away from your home.
Deferring for a term in the hope something comes up via the waiting lists might be a sensible way ahead. Accept the offered place for now, think about deferring, find out where you are on waiting lists (remember you can go both up and down, as they are ranked by his well you fit the criteria, not time on list), and investigate childminders who do school drop offs and pick ups and whether there is before/after school care available. Also see if there can be any flexibility on your working hours. If you can shift them so you can always do either drop off of pick up, and therefore need to sort only one end of the day, can make your admin somewhat less onerous.