A custom report should be able to do most of what you want, but there are some challenges.
Custom Reports are in MLS in the Reports/Forms screen, or on the Membership menu.
The challenge you face is that custom reports are oriented towards individuals, not households. You can try to compensate for that by adding a criterion (Household Position -- is -- Head of Household) and including the "Head of House and Spouse" field instead of the Preferred Name. That would let you report on households and their home teachers. But doing it that way would not allow you to report on visiting teachers, because for every household with a male HoH, you would be essentially reporting on him, and of course he wouldn't have visiting teachers.
You could report on all the adults in the ward as individuals (use a criterion such as Age -- is or is greater than -- 18, or something like Household Position -- is -- Head of Household -- or Household Position -- is -- Spouse). That would allow you to show home and visiting teachers, but you would lose the household grouping.
Another possibility that might be the best option would be to report only on women (Combine a criterion for Sex -- is -- Female and the criterion for Household Position being HoH or Spouse I mentioned above). Then you could report on HT and VT.
Questions that can benefit the larger community should be asked in a public forum, not a private message.