No it doesn't make any difference. For the registrars it is completely normal to deal with applications from abroad. However, remember that there will be a registration fee for each school and these can mount up quickly.
Any idea where you will be living? Where will DH be working? Beggars can't be choosers, but a short school run will make your life much easier as the youngest children often finish school at around 1.30 - 2pm. They start at about 8am.
Jebel ALi and JPS are quite a way apart although both close to the Sheik Zayed Rd.
I would say little point in applying for either JESS school as they have waiting lists for years ahead, but they give details on their website - JESS is an excellent school.
Unfortunately reception is one of the hardest years to get into.
I suggest you try Wellington - another good school.
If you are prepared to consider an international curriculum IB primary years , consider GEMS Dubai World school
Kings is likewise excellent. Repton pretty good too.
Just be careful of applying to every British school. Some are nominally British but will have a more Indian bias. DESS is a good school, but is much nearer the old town and away from the most popular expat areas.
Best advice is to speak to the registrars and they are normally very helpful.
Also become a disciple of expatwoman.com. THe ladies on there will have up to date info and experiences and the site has a list of schools and their fees - a mine of information.
Schools is just about the worst bit of moving to Dubai. Once there I'm sure you will enjoy it. We did for 8 years.
Any specific questions, I'll try and help.