What aniani describes is common, but the children don't want to live with their mother in your case.
I assume both children are yours, either biologgically or by adoption.
The courts will always make sure the children's needs come first and will not disrupt them where possible.
In your scenario it would be fairer for the children to live with you in the family home, while she moves out. The house sold when the youngest is 18 and any equity divided equally. Or for you to buy her out fairly now.
She can't make the children live with her - they are old enough to make their own decisions.
You need to see a solicitor if she will not see reason.
Is her name on the Title Register of the house? If so she is a joint owner of the house regardless of how much money she has put in to it. Even if her name isn't on the Title Register she will still be entitled to a fair share of the equity as she is your wife and she raised the children and supported you in other ways.