Of course there are times you'd choose your partner over your children and it would be relatively uncontroversial. Especially with adult children, it depends on circumstances and who has the greater need. For example, if you're on a date with your partner and your child calls you just to chat, you'd likely say you're busy and ask to talk later. If you're on a day out with your child and you get a call that your partner's been hospitalised with a serious injury, you'd cut the excursion short and go to the hospital. You get the idea.
In THIS case, though - especially given that your children are adults and presumably don't live with you - the position they have taken is extreme. If they dislike your partner or don't want to be around him or don't trust them, they could reasonably say that they will not see HIM - they won't go to your shared house, only agree to see you at their house or out, won't invite him or agree for you to bring him to family events, etc. Instead, they're not just cutting HIM out but severely punishing you for staying in a relationship with him.
You say I was clear in saying that DP was in the wrong but DC wanted more from me; what exactly did DC tell you they wanted from you? It sounds like your DCs feel like you are betraying them on some fundamental level by remaining with your partner, not "just" that they don't want to be around him or think you have bad taste in men. You MUST have a gut idea about what's going on here - do your DCs have a history of ganging up and trying to control your life to an unreasonable degree, and if so, why wait so long for this ultimatum? Or is it more likely that what DP has done is much more serious than you are admitting to yourself, and/or that the reaction is not just to this one incident but to something bigger and more substantial?
I don't know who's "right" or "wrong" here but it's a terrible situation. Unless you can see that your partner has done something unforgivable, it sounds like either choice is going to be heartbreaking for you and your relationship with whoever you DO choose may not ever be the same again.