Yes, kissing a child on lips is a bad thing anywhere anytime
It can and almost surely will transmit the herpes virus. No method eradicates the herpes virus from the body. Once you have it, you keep it for life.
Living with herpes outbreaks is painful and stressful. For some individuals the outbreaks are mild and rare, for others they are frequent and severe. The virus can easily migrate from the mouth area to other parts of the body like the inside of your nose or genital area by simple contact (you touch your mouth when the virus is shedding, which you would do as it is itchy before it gets painful, and then touch your eyes or re-adjust your sweaty pants: the virus migrates nearly instantly).
For these reasons, do not share towels and do not leave your used towels around for your child to wipe their hands with.
Just how likely is it that you are infected by a strand of the herpes virus, knowingly or unknowingly? Very. The infection rate is thought to be as high as 90% in some regions for some categories of people (women having greater infection rates). You can check your odds here (if you don't already know your infection status): https://en.wikipedia.org/wiki/Epidemiology_of_herpes_simplex
If you want a visual, search for images with the keywords "herpes baby" or "herpes child".