This is a really difficult situation for parents but one the Court really has little control over. We have to trust the best judgement of the parent with the new partner (which sometimes is better than others). The Court will take into account the reality of new partners and new living arrangements and expect parents to be sensitive but accept children should and must adapt to the changes in the family. Unless the presence of a new partner is likely to cause harm to the children i.e. serious emotional distress or if the new partner is violent, abuses substances or has certain convictions, the Court will be reluctant to interfere.
I always advise parents to ensure that they always spend quality time alone with their children and are sensible about what their children see and do with the new partner. Take into account their age and understanding as what is acceptable for a 5 year old is likely to elicit a very difference response from a 15 year old!. To ignore children’s feelings on this can be very detrimental to contact. Likewise, the other parent should recognise that the presence of another adult can sometimes make contact more comfortable for children and another interested and affectionate adult can make it more enjoyable. Children do not need a stream of new adults passing through their lives so parents should only introduce partners when in a committed relationship. Friends are fine but make sure you behave like friends and keep an eye on how comfortable your children are.
Ultimately, the Court cannot compel a 3rd party to meet a parent. Talk to your partner about why it would help you and the children to meet the new partner. He or she may just think you want to cause a scene or talk badly about him or her to the new partner. However, bear in mind it may not be your ex who is the sticking point. The new partner may be happy to have your children in his or her home when they are with their parent but see the rest of your family life and your relationship with your ex as nothing to do with him or her and something he or she would prefer not to get involved in.