I am looking at this from a legal stand point only. I do not have experience of children with special needs and only you as parents will know how such a big move will affect your children.
Firstly the fact it is a non Hague country isn't that big a deal. It sounds as though your ex allows you and the kids to holiday there now which is as big a child abduction risk as your desire to move permenantly. The matter could be dealt with by your local family court.
You have to attend mediation before.you make an application to Court. Typically each person pays for their own mediation. If he wont pay and you don't want to pay his share mediation will.come to an end and the mediator will sign the form c 100 to allow you to make an application to the court for a specific issue order that you be allowed to remove the children from England and Wales.
When making a decision the Court will look at what is in the best interests of the children. Typically when the resident parent is in a long term relationship and has given careful thought to contact with the other parent and educational arrangements the resident parent is allowed to take the children out of the country. To make.your arguement as strong as possible you will need.to outline how long you have been in a serious relationship, how long you have done the long distance thing and how it.impacts upon family life. How you would facilitate direct contact (twice a year for 2/3 weeks etc) whether you would be prepared for dad.to see the.children if he were.to come to your new country to visit them once or twice a year. How often they could skype / face time.
Legally your biggest hurdle is going to be your children's special needs, how their educational needs can be met, and what detrimental effect if any a change of.schools and.change of.contact with Dad.will have on them.
It is essential that before the matter.goes.to.court you have.child school places available for all children so you can provide this information to your ex and the Court. In places likes the UAE getting school places at all can be difficult and.provision for special needs.is almost non existant (depending on the level.of need). You may also want to.speak to the.existing.school and see what their thoughts are on how a move would.impact the kids and what they feel would be the minimum level of support that would need to be in place in a new school.
In short what you are asking for legally is not that contraversial provided you have dotted I 's and crossed t's in terms or proposed contact and education.
You must be prepared for ex to say that you can go and he will be the resident parent of all the children and.you can see them when you visit the UK. You will need.to have.an argument ready as.to how remaining.in.your care.on a.different country would be less.disruptive to the.children than moving.to be.with their dad.
If mediation is unsuccessful the Court will aim to make.a.final.decision within 6 months. It maybe that the academic term in the new country also.starts in September so you would need to start mediation rolling sooner that later to get everything resolved by then.
Sorry for all the. Fat fingers.