When users are looking at our help, if they clicked on search, the next time they will open the help link, they drop into the search tab (which is shown empty).
I would like that users will go to the TOC tab every time the help is opened (help.mydomain.com) is there an option for that as a URL (like in filters)? Maybe an option to disabling the browser caching of this specific thing?
If no out of the box option available, would you recommend looking into scripts for doing that?
To the best of my knowledge there is no built in option or known way of achieving what you want. It is, as you have realised, a browser caching issue There are various offerings on Google for that but from what I have been told, they don't always work well. One person I know of eventually found they had to get their web server configured in a certain way. I don't have the details.
See www.grainge.org for free RoboHelp and Authoring information.