Is there a tool to visualize the citation network which works with Google Scholar? I know about tools like CitNet Explorer and VOSviewer, but they only work with Web of Science, which doesn't contain many papers I'd like to have in the network.

Is there any software, which does the same thing with data from Google Scholar?
To my knowledge, at the time of writing, Google Scholar does not define an API to access data, so presumably no software exists. Beyond Google Scholar and the tools you've already mentioned, you could try  https://www.semanticscholar.org or https://aminer.org. (I'm a little unsure what you mean by citation network, so perhaps they don't satisfy your needs.)