If you are living in the UK, it may be better in the long run to divorce there. Dominican divorces are not unilateraly accepted in all countries (or in all states in the US). Even quicky celebrity (sp?) divorces done in the DR are usually followed up by extensive legal paperwork in the home country. Also, if the property is in the UK and any issues come up, you'll be wanting to get it taken care of there. Ditto with the children, there may be modifications that happen later that will much easier to handle in the UK, through the same court. Also, if you have to enforce or need police assistance that requires verification of custody agreement, they are more likely to do so at face value. If you are asking for child support, again, I would imagine that the chances of getting it and enforcing it are greater in the UK.
Without knowing all of your circumstances, the only good reason I see to divorce in the DR is because you are living there. If someone has suggested it is faster, cheaper, or easier, I wouldn't be swayed that easily.
So sorry to hear your story, it's a difficult process, but one that you can survive and recover from. Wish you and your children the best.