Yes, since you are paid hourly - that would be one of my big talking points when going to the boss, i.e. how the remote switch would save them money and (and to a lesser extent) you time on your off days. Win-Win! Put yourself in the shoes of your boss. Whatever your boss would be uncertain about, take steps in your discussion that acknowledge those areas as best you can.
To add to part of what Fishindude said, it is true that many of us need structure and to separate work from non-work. I certainly do. Your odds of having a sustainable remote situation (like for yourself if this was hypothetically approved) go up if you have a designated area of your home that is for work and out of the way during your leisure time and especially anytime you are entertaining. i.e. a designated room for your home office with general office amenities (printer, copier, scanner, fax, dual monitors, file cabinets, shredder, organizer stationary, etc.) will generally be MUCH better than the old laptop on the couch trick.
To the other part of what Fishindude said - not every job can be accomplished remotely. But for those that can, it makes sense to at least try it out on either a part-time or full-time basis with some of your best performers that are seeking this out (unless you are fine with them leaving to seek more flexible arrangements elsewhere, in which case I'd argue the employee in question either was replaceable enough or did not possess enough value in your eyes to keep them).
The boss has the right to revoke the privilege at any time and there should be objective standards to monitor performance. If a boss approves a remote situation and the employee isn't working like they are supposed to, the employee can be counseled, put on a PIP, have the remote situation changed, or simply be let go depending on the severity. But part of the onus is on the boss as well to have performance measures for the remote situation, just like they would if they were in the office.
Communication is key, utilize videoconferencing, screensharing, instant messaging, and good old fashioned phone calls (I prefer email as a slightly more formal communication space that isn't cluttered with threads that are essentially text messages, YMMV). Whatever fidelity would be lost by not seeing someone in person - there should be a reasonable way to substitute (not replicate, per se) the experience (if not, then maybe remote work is not appropriate for that position). As boss, stress that it is a privilege and you are putting faith in your best-performers to get the job done just like they always have. In my experience, this real talk from the supervisor garners a little extra buy-in on the overall mission from the employee and makes the employee a little more accountable and do not take the setup for granted.
As for the distractions at home, I agree this is not acceptable. Kids go to school or are at daycare or being watched as appropriate by someone other than the employee. Remote work is not a loophole to make other aspects easier while working.