It would help to know more, as others noted. The tone of your post indicates to me that you and the mom clearly are not friends and don't really communicate other than perhaps about details of your sons' meetings--is that accurate? Do you ever talk with her on other subjects, or spend any time chatting with her in other circumstances--?
You say you've "watched the other boy do countless chores." So the mom actually has you and/or your son stand there and wait while the son does these chores in front of your son, you and mom like you're witnesses? If that's the case, it seems as if she's almost intent on punishing or shaming him in front of others; chores are not shaming in themselves, of course, but telling guests to wait and watch while her son chops down a tree, and making a get-together dependent on how well he "performs"? Did you see this one with your own eyes too? How does the mom react: Is she beaming with pride as in, "See how strong he is, he's such a good kid" etc. or is she glowering, as in, "Well, we all have to wait now while Billy does this and he knows you have to leave if he doesn't hustle!" In other words -- please let us know how this mom seems to be acting when she's doling out these chores. So she's really having him do them with his guest and his guest's mom standing right there, waiting for completion before guest and her son can see each other?
If that's the case -- that is troubling.
But as others noted too, the boy may be different with her from what you see of him with your son. There may be disciplinary issues that the family resolves by having him pay for any fun with chores. I'm not saying that's sensible or works, but you and I don't know the back story, if that's what's going on.
How were you told that your home isn't the environment she likes for her son? Did she tell you herself or relate it through your son ? The former would be at least decent of her, but if she told your son that, she was out of line; that's an issue for the adults to handle, not the kids. Did she give any details, or did your son if he related that news?
So many questions here and some depend on your own home situation and whether she has any reason to not want her son at your house. Those reasons may not make any sense to you but may make some twisted sense to her--though that does not mean there's anything you should change.
Sounds like she has her son on a very short leash. Does she do this with other kids or is your son the only friend her son has? I'm guessing yes....As for what you and your son should do: If this other boy is an OK kid with a really strict family, and your son's his only friend and your son also just likes him -- I'd try to keep up the friendship somehow if your son is up for that. This kid may need the friendship more than you know. It may be decided for you, though, if the mom is now saying she doesn't want her son at your home; the natural corollary to that is her saying next that your son isn't welcome at her home either.