I purchased the SlingBox PRO-HD a little more then a year ago. If you have and HD TV set up at home, then you will want the Slingbox HD-Pro. THis way your husband can watch HD programing while he is away from home. I love my SLingBox for watching my local NFL team's games and stuff I have on my DVR while I am traveling.
You are correct. If your husband wants to watch slingbox on his mobile devices (phone, tablet, etc) then you will need to buy the slingbox apps for those. I think they run about $30 for the apps. Good luck with what ever you decide.
Just to add that your only real choice is between the Pro-HD and the Solo. The big difference is that the pro-HD has a built-in tuner so you can watch TV programs without disturbing the hosts of the Slingbox. BUT, that applies only to unencrypted channels. Basically, if your Mom just plugs a co-ax lead into her TV then the Pro-HD tuner will work fine so go for that. If she has to plug the co-ax lead into a cable/satelitte box and from the cable/satellite box to the TV, then the tuner will be useless and you might as well buy a Slingbox Solo. Also, note that if your husband wants to watch a different channel to your Mother and she is using some sort of cable/satellite box then you will have to rent an additional cable/satellite box for the Slingbox.
Also, the 'HD' part of Pro-HD is a bit misleading. What it actually means is you can plug in an HD source and watch it in HD LOCALLY, i.e. on the same network. If, however, all your viewing is done from a remote location then you will not get HD, and the quality of the stream you get will be controlled by the upload speed of your Mother's Internet setup. In that case, again, you might as well go for the Solo as the remote stream from the Solo is very similar to the remote stream from the Pro-HD.