Then I don't think that you have anything to worry about.
You asked when children get to make the decision, and the simple answer is "never". They aren't parties to the litigation and they are minors,
I've done work for my provincial Children's Lawyer office so I know what I'm talking about. Everyone thinks that age 12 or whatever that children can choose. They can't. At certain ages, children's consent is needed for adoption and at a certain age (12) they can be charged with criminal offenses. But they never have the right to say what the custody and access regime should be, unless the court gives them that specific right.
Having said that, when the kids are getting older the court may well want to know what the kids want, and why, and how firmly they want it, and whether they are being influenced. That's where your provincial Children's Lawyer can be called upon to send a lawyer or social worker to interview the kids and look into it.
You're clearly worried about the kids saying that they want to live with him. This is a good opportunity to tell the kids that it's not up to them, rather up to mom and dad. Father might have told then that they can go him if they want, but it's time to tell dad and the kids that this is simply not true. If you have a lawyer, have them write to dad and tell him to knock it off.
It's true that as children get more mature and more wise that the court will want to know what they want, and after a certain age (depending on the child and the circumstances) the court knows that it can't make the child do anything that the child is adamant against. But you're not there yet. It's rare for a court to leave even access up to the child at age twelve.
In fact, depending on your evidence you could use this as why you should have sole custody. It's not in the children's best interests for dad to be saying to them that they have the right to choose.
As you may have heard, children have a voice but not the choice.
Yes, I'm here. I've been typing. I know that the site is set up like a messenger, but you can't see when I'm typing.
Dad is pretty clearly trying to put pressure on you about his arrears.
Comment or question?