The law says that children are entitled to have a relationship and contact with both parent sand the courts will enforce this if necessary
There is no longer any such thing as custody and access or even residence and contact - it is about a Child Arrangement Order setting out how children spend their time with each parant
You have Parental Responsibility for the children which means that your ex is not entitled to take the children out of the oc**try without your agreement or an Order form the Court.
In addition the fact that you have such regular contact with the children means that if she tries to move away to stop this then you can apply for an order forcing her to return until the court decides whether the move is in the best interests of the children - and how their time with you can be preserved.
There is no reason why the children should not spend nights with you - and there is no doubt that a court will grant this if an applictaion is made.
There is little chance at present that you would be able to take on the main care of the children - however if you start overnight contact on alternate weekends plus one (or even two) nights in the week and they thrive in your care then there is a possibility that in a years time it could be possible.
The starting point is to try and discuss matters with your ex using family mediation
If that fails or she refuses then you can apply for a Child Arrangement Order using a Form C100 and paying the fee of £215
If she does move then you will be able to trace her and the applictaion can still go ahead
Please ask if you need further details