Thank you for your question
My name is Clare
I shall do my best to help you but I need some further informtaion first
If they go ahead with the move would you wish your sons to live with you?
Then your options are limited in terms of preventing the move.
You can certainly apply for a Prohibited Steps Order to stop the move happening until the Court has decided whether or not the move is in the best interests if the children but unless you are willing to take over their care then the Court has little choice but to approve it - as otherwise technically if the mother decides to move regardless then the children will simply go into foster care in the area. If your ex knows this then she can simply bluff it out
You do have more control over the issue of travel for contact - if they are moving then it is reasonable to expect them to take on the time and cost of ensuring that regular contact is maintained - and you can apply for a Prohibited Steps Order to ensure that the move does not take place until this issue is resolved.
Of course this may in fact be all that is needed to prevent the move given their reluctance to facilitate contact in the past.
The Prohibited Steps Order is dealt with by way of a C100 and given the urgency you do not need to attend mediation first (unless you wish to)
I hope that this is of assistance - please ask if you need further details