Following up on an idea Mrebo and PeterPan discussed in the Prequels Redux thread, I’ve just watched the relevant scenes in my TPM rewatch and I think it’s possible to make it so that Qui-Gon frees both Anakin and Shmi. After the podrace in their house Qui-Gon says both of them are free, Anakin starts celebrating that he can train to become a Jedi, he asks if Shmi is coming with them, Qui-Gon gives Shmi a look that Anakin doesn’t notice but Shmi understands, and Shmi explains that her place is on Tattooine and she’s not going with them.
First of all, why bother doing that? Well, I think that it helps drives a few points home. It shows us the disparity between Qui-Gon’s ethics and those of the Jedi Council, instead of simply having Obi-Wan tell it to us later on Coruscant. It makes it clear that (in Mrebo’s words) “she is left behind because the Jedi don’t make allowances for parents tagging along,” but also that Qui-Gon is the kind of person who would free her anyway, while still understanding the difficult position it puts them in. All of this supports the thematic idea that Qui-Gon would have been the right person to train Anakin successfully, because he isn’t as dogmatic and black-and-white-morals minded as the Jedi Council. Anakin needed understanding and flexibility, which the Jedi didn’t offer - but Qui-Gon certainly seemed like he would have done.
It also means that Anakin’s frustrations with the Jedi arbitrarily forbidding him from seeing his mother in AOTC serves to highlight the whole “Qui-Gon and his lackadaisical approach to the Jedi Code was the right way to do things” idea, by absolving Qui-Gon of being (in retrospect) a complicit arm of the Jedi Council when it comes to Shmi, and Anakin’s attachment to her.
Basically, the Jedi being actually pretty terrible is a big part of Anakin’s fall to the Dark Side, and if you want to enhance the themes of Qui-Gon being the only one who’s really got the right way of doing things, it helps to make it about “the Jedi won’t allow attachment so he can’t even check on his mum” instead of “Qui-Gon was fine with leaving his mother a slave if it meant getting a strong Force user for the Jedi.”