In this case it’s up to you to decide whether your children have a real grievance with your new partner.
If they think he or she is ‘uncool’ for example, that’s not really a reason for you to end your relationship. In this case it’s likely they’re being vocal in their dislike because they feel they have to compete for your attention.
Of course, if your children have a more substantial dislike then you have to consider their feelings. But remember that this is your relationship, you make the rules, and this is about your happiness as well as theirs.
After all, if you’re happy you’ll be in an even better position to make your children happy.
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