maybe you need to have an honest think about who objects to the new girlfriend: your children or you? if its them, its probably because you have bad mouthed her or not accepted your part in why the marriage broke down. its tough when your children get to meet her for YOU but accept it and focus on thier needs not yours.
Mine are 13 and 15, 13yo is ok with dad but 15yo goes through periods of refusing. He has now applied to court for a contact order for 50% contact, which they don't want. The children have to attend the hearing too. I do not force either of them to go, but he sees it as 'his' time, not their weekend with him, but his entitlement! DD1 is here right now when she should have been with him.
In the absence of a contact order, your children are old enough to choose. I think their dad should see them alone until they were ready to meet OW. It is very unlikely my ex will get a contact order for either child, certainly not for DD1 as contact orders expire when the child is 16.
They're old enough that their views would be taken into account if their father wanted to take it to court but one would hope that their father would be sensitive to their wishes and not let it get to that point. There is the danger that he might feel you are unduly influencing the children in their decision.
Can my children say no to visiting their father is his new partner is going to be with them? They don't want to see her as she was the cause of our marriage breakdown. They are aged 12 and 14. Can anyone offer advice please.