We are planning to travel from Mannheim to Heidelberg and then on to Baden-Baden on the same day. Could that trip be covered by a Lander ticket for Baden-Wurttenberg for my husband and me and be bought at a machine at the station, for 28 euros? Would that enable us to use any train after 9 am from Mannheim, and then later any train from Heidelberg heading to Baden-Baden?
Yes.
As long as those are regional trains (IRE/RE/RB). Länder-Tickets are not valid on long distance trains (ICE/IC/EC).
Find the schedules on the German Rail website. Be sure to check "only local transport". It looks like it would be an S-Bahn from Mannheim to Heidelberg, another S-Bahn from Heidelberg to Karlsruhe, and a regional train from Karlsruhe to Baden-Baden.
All of those towns, Mannheim, Heidelberg, Karlsruhe, and Baden-Baden are in the state (Land) of Baden-Württemberg and therefore covered by the same Länder-Ticket. The Baden-Württemberg-Ticket also covers travel to the left bank of the Rhein, in Rheinland-Pfalz, between Mannheim and Ludwigshafen, and Karlsruhe and Wörth, and between Ludwigshafen and Wörth, so you could go from Heidelberg to Ludwigshafen, through RL-P to Wörth, then to Karlsruhe (not that you would want to, but it is possible).