Not a dumb question whatsoever. It all comes down to finding the best connected device that works with Home B. Your options for a connected device comes with compromises and as with all things sling, they're still a work in progress. There are a few directions you can go in.
One, the WDTV Live hardware that has the slingplayer app built in. Two of those hooked up either wirelessly or through ethernet will get you connected to your slingbox. Downsides are the interface which requires a lot more effort in accessing the functions ( DVR, fast forward, etc ), but it does the job. Other's have reported buffer delays with the remote functions, but from my experience, and a lot of others, it's mostly a stable stream. Added to that, the WDTV live will include apps like Netflix and the ability to run an external hard drive full of AVI, MP4 and MKV movie files that you can connect to it for entertainment. Obviously you'd need two of those to cover both TV's in home B and the most negative things I can say about it is the interface for the WDTV live is a little sluggish and clunky, but it works.
Second option is a GoogleTV box ( There's three that I know of and a Netgear googleTV box that was shown at C.E.S ) The Vizio Costar, the Sony NSZ-GS7, and the hisense pulse. The Hisense pulse is the newest, but has so-so ratings. The Vizio was horrible to begin with, but has improved firmware making it more tolerable and the Sony, which is what I also own, has a few bugs here and there, but does a pretty good job at sling streaming. It's more complex to learn and to run than the WDTV live, but has the benefits of a chrome browser built in for web-surfing, google music access, etc. Same interface as the WDTV live for the slingplayer, but the touchpad on the GoogleTV hardware make it a little easier to navigate.
If you want an easy setup and something that's not complicated to run ( in comparison to a GoogleTV box ), I'd say go purchase 2 WDTV Live boxes. You don't have to get the WDTV Live hub box which has a 1TB hard drive attached to it, the basic model will do.
The main thing to point out is the stability of both internet connections at both houses and the upload speed of your slingbox connection. That will dictate the quality and the experience you're going to receive from a connected device.
P.S The Logitech Revue is a first gen googleTV box also out there for sale....even though it's discontinued. Don't go anywhere near it for Slingplayer use.