I love the Clorox oxygen cleaner for stains. OxyClean is good, too, but the Clorox brand has worked best for me. Be sure to test it on a spot of carpet that's out of the way (like under the sofa) first to make sure it doesn't take the color out, though. I haven't had any problems with it, but you never know with different materials and dyes. As far as an odor neutralizer, just check the ones at the pet supply store or even someplace like Lowe's or Home Depot, who very often carry industrial cleaners in smaller containers, and pick one that you don't mind smelling for a little while. Dogs tend to dislike citrus smells, so that can be a deterrent to using the carpet, too. Lowe's or Home Depot will probably have a good all over odor neutralizer that you sprinkle down then vaccuum up later, too. One with baking soda is good, or you can get one that doesn't have it, then sprinkle a box of baking soda on your carpet along with it.
It might help Sawyer get the idea about inside/outside if you take her accidents outside and put them where you want her to go, taking her with you on a leash so she can see where you've put them. I've found that the puppies usually have to go after they've eaten and played for awhile. When they calm down, it's usually about five or ten minutes and then they need to go. That might be a good barometer with Sawyer, and if you play with her (which I'm sure you do already) it will not only give you an idea of when she needs to go out, it will help give her more confidence about her place in the world. I've never owned a Beagle, but I've been around quite a few, some were pets and others were working dogs, and it seemed that they were very vulnerable to being bullied, perhaps because they have such sweet natures and are so focused on pleasing. They really are loving, gentle, playful little dogs - sometimes too gentle! I've gotten very angry more than once seeing a parent allow a child to torment and bully the little creatures, knowing that they won't defend themselves!
By the way, you might want to get her a harness to use when you walk her. I've found the dogs seem to be more comfortable and feel very secure with one and it gives me more control over pulling without having to use a choke collar - and with my brutes that's important. My thinking with a dog like Sawyer is that the control without the pull of something directly around her neck will be more reassuring and less dominating than a collar for walking. Of course, in town you still need to keep a collar with her tags on her at all times, but I'm really sold on using a harness with a leash.
You're really going to love having a Beagle in your life; they are just so completely loving.