Kids that are missing a parent tend to always wish and hope that the missing parent will come back. If a new person appears in a parental role then the child may see him or her as a block to the real parent coming back.
It is almost inevitable that your kids will resist you dating or meeting new people simply because humans are hard-wired to be attached to the original parent. However there are some things that you can do to avoid the worst case scenario of your kid resenting you and absolutely hating who you have chosen to bond with.
There are several ways to introduce your child or children to your new mate to avoid the worst case scenario.
First of all accept that there may be some protests and don't stress about it. Address your child's concerns but don't argue with him or her. Recognize the hurt feelings but do not argue with the child so a dramatic situation can escalate.
Be very clear and explain to your children that just like they need playtime with other kids you need to spend time with other adults.
Encourage the child to express any feelings of distress but make it known that their emotions and opinions will not dictated the course of your love life. If the child feels neglected show through your actions, not promises, that you will be spending more time with him or her. Never promise a kid that they will have final approval of whoever you are with.
Make sure that the introduction of your new significant other takes place only after you have prepared a bit of groundwork first. Get your child used to the idea that you will be meeting him or her soon.
It is also best to take the drama out of a first meeting by making it very casual. Your first date should be focused on an activity and not on people. It is a good idea to do something like meet at a playground or go to see a movie or baseball game. This will help enhance your child's positive associations with the person.
You could be dating the best new Daddy in the world but if your kid does not like him your relationship could turn into a living hell. If your child is resentful, depressed, failing in school, rebellious or even violent as the result of your actions you have two options.
1) You can end the relationship. Unfortunately this may be your only recourse if you see that your child is truly going to be screwed up as the result thing of your actions. Self-sacrifice is usually part of being an adult. You might have to wait until your child is more mature or psychologically able to handle a new person in a family before you start dating again.
2) You can try taking the child to therapy which often works to help accept the newcomer into your family circle.
There is no absolute wrong or right in this sort of situation. It is up to you decide whether or not a new relationship is going to be worth your kid's sanity or if you can be patient and wait until the child is better adjusted before dating again. In this case, it is not about letting the child run your life or giving the kid all the power. It is about being flexible so that your child grows up healthy.