You've been divorced for several years. You've been busy with your job, young kids, and trying to keep ahead of the household chores. You've got a few good friends but, the truth is, you've also been longing for intimacy. At last you've met someone special. You're delighted to feel those loving feelings again, to know you are special to someone who is over the age of 7, to have an adult to share things with, to hug and cuddle and maybe have sex with. He, or she, is wonderful! You're in love. You're sure the kids will love this wonderful person too. Right? Probably wrong!
Unlike you, the kids haven't been longing for a new person in their lives. As far as they are concerned, their life is complicated enough. They love you. Unless there's been abuse, they love their other parent too. They have all the adults they can handle.
Unless there has been abuse (and sometimes even when there has been), kids usually want their own parent back in their lives and yours. A new partner for you jettisons any fantasy they may have had that you and their other parent may get back together.
Your kids have had you to themselves for awhile. They're not crazy about sharing you. Don't expect them to be happy because you are. Children are wired to be self-centered. Yes, in theory, they want you to be happy, but not if it means that you are distracted and less available to them.
However much fun or caring the new person may be, the kids are at best ambivalent about warming up to him or her, especially if they've already had the experience of being introduced to someone who didn't work out. From where they sit, your last relationship didn't last. Why should they invest in this one? They may protect themselves by not getting too close.
On the other hand, even if they do like your new true-love, they aren't going to like taking orders from yet another adult. "You can't boss me. You're not my real mother/father!" is a predictable refrain.
Kids from about 10 up may be uncomfortable with displays of affection. Tweens and teens are coming into their own sexuality.They may not be able to handle evidence of yours.
Does all this mean you should remain without a loving and loved partner for the rest of your life? No, of course not. It does mean that it takes good timing, patience, and empathy on both your and your partner's part to fold him or her into your children's lives.