We went through this as my dhs ex applied to move to Europe with their children.
It had to go through the courts as it was the only way to ensure that a fair agreement was made. Past history meant he wouldn't accept her word.
The courts insisted that she had to show that she had really looked intot he whole process, how she (and her df) would support the family. How they would be able to afford to live etc.
Also she had to show excatly what she would do to ensure that the children would maintain contact.
We ended up with a court order specifying weekly phone contact (took it in turns to phone) and contact every holiday. We agreed to share the travel costs. In our case they moved to France so they brought them over from France and we met them at the ferry terminal and then we took them back to France and they met us at the ferry terminal there.
If the whole family came over for the whole time then we paid half the travelling costs of the ferry as we then didn't have to do the trip.
The judge told us that as it was only Europe there would have to be a very good reason for him to say no. But he was strict about pointing out to her that she had to make sure that there was regular contact.
Obviously we couldn't do much if some of the court order wasn't complied with - such as if they didn't phone when it was their turn or provide us with written reports of their wellbeing etc.
But to be fair we did always have the contact with them at holidays and often ended up with longer than the court order specified.
We also had it written in that if they ever came back to the UK for any reason then they had to let us know so that dh could see the dc and vice versa if he went to France.
As long as you have done al your homework and have all the paperwork to back up your application you stand a good chance. Show you want to be fair with visits and contact. And be prepared for the legal bill