Hi, thank you for your question. Just a bit more information required to fully assist you:
-Has there been a court approved financial settlement, if so what are the terms?
-Whose name is ***** ***** title of the property?
-How old are the children?
You can check the title deed on the property here: https://www.gov.uk/search-property-information-land-registry
If it is in joint names you both have a legal interest in the property, but if he has moved out and you are solely occupying it, he cannot prevent you from having your partner at the property. In relation to the children, he can object to them having contact with your partner and there will need to be discussion on how this, if at all possible, will progress if he is a long-term partner.
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As you have a legal interest in the property and he is not excercising his right to occupy it he cannot dictate how you use it and whether your partner resides there or not. If your ex-husband is contributing to the mortgage he would be entitled to seek occupational rent as he is not enjoying the use of it, but other than this it will be difficult for him to attempt to exclude your partner from the property.
As he has a legal interest in the property he can move back to occupy it at any time and this can only be prevented if you were to obtain an order from the court, such as an occupation order.