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You could not force the mother to move.
The issue is whether you can convince the court to allow you to move the children.
And having sole custody does not give you the right to move the child.
Rather, you will need to get a court order unless the mother consents.
You will have to prove to the court that what you want is in the children's best interests.
Given your post your case is stronger than most so it is possible though not at all definite that you could succeed.
Does that help?