There shouldn't be any reason to worry. Just treat it like a small puncture wound: she just needs to clean it out with peroxide and put Neosporin or Betadine in it - and then stop hitting the dog!
I'm trying to remember how big Frodo is: I'm thinking he's a small dog. A shot of water from a spray bottle or shaking a can with some coins or rocks in it will do more good than hitting him, and he shouldn't react aggressively to either of those things.
Your housekeeper has now trained Frodo to think that there's a good chance she's going to hit him when she approaches him, especially if there's a trash can in the room. I hope she'll try to fix that by spending some "friendly time" with him and give him the occasional treat.
Charley's mother had a housekeeper that came in once a week when Buffy was a pup. Vergie was hateful to Buffy and Bimmer - until the day she made the remark that Buffy was about as big as she was going to get (about the size of a large Rottie) and Hazel, the lady who came in and took care of Charley's mother every day, laughed at her and told her Buffy was only 6 months old and was going to get a lot bigger. Vergie was a lot nicer to Buffy and Bimmer after that! lol!
