First to answer you question I don't know any such website or software that can do the job exactly as it is needed; I have long searched for the same and I haven't had enough success.
There are some which will work but I can't offer you any specific one at this moment. I'm also looking for some suggestions from other members.
Further another logic is that if there were such perfect/professional website creating software or websites then those thousands and lakhs of website designers would not have any job.
But yes with technology updating so fast it might be possible. Still to the best of my knowledge such a software that you are looking is not available. There may be paid versions but still they won't do half as good as real web designers.