Rewatching ep 1 with my son.
God, Everyone just forgets about Shmi. Padme is rich, and doesn't take action, the Jedi could send a courriour, and don't, Anakin waits a decade...
Palpatine could buy her, and then use that to drive a wedge between Anakin and the Jedi...
But everyone just forgets the virgin Shmi.

As far as the Jedi go, they have a thing against attachments and from their perspective they already have enough of an uphill battle to basically get Anakin to let go of the fact that he has a mom somewhere out there, without the possibility of her being free and maybe actually showing up at the temple wanting to see him or something.
Not gonna go into how fucked the jedi's philosophy is about that, that tauntaun has been beaten to death elsewhere on the Internet.
Sure, the Jedi aren't exactly big fans of slavery, but putting aside the attachment to Anakin, she's just one slave out of how many millions? Billions? Trillions? In the galaxy. Sure they can go around buying and freeing slaves whenever they come across them, but ultimately that just creates a market for slaves if slavers know Jedi will just buy up their whole inventory at every chance they get. That's the kind of thing that needs to be tackled at a deeper level.
As for Padme, sure, she could probably have arranged for it, but I think it's pretty likely Obi-Wan took her aside at some point and said "look, it sucks, but we really can't have Shmi getting in contact with Anakin, it'll fuck up his training and he needs to do the whole 'chosen one' thing, so it's really for the best if she stays there on Tatooine" Whether that's actually the case or not, that's probably what the council believed, and obi wan would go along with it. And if Padme hears that coming from, honestly, probably any Jedi, they are, after all, supposed to be sort of paragons of peace and justice and all of that, but especially from obi wan, a Jedi she personally knows and trusts, why should she question that?
Probably also some logistical and political hurdles in the way. Most of Padme's wealth is probably in Republic credits, which watto wasn't too keen to take as payment. I'm sure some sort of currency exchange or other trade could have been figured out, but imagine the scandal if word got out and someone put the spin on it that she was laundering money to purchase slaves? That's quite a potential minefield to navigate.
As for Anakin himself, he was still a Padawan, a fairly senior one who could be trusted with at least some solo missions by the point he finally went back to find his mother, but still a Padawan, so I'd imagine he didn't exactly have leeway to just head off to the outer rim to get his mom whenever he wanted. I'm honestly not even sure if even most full-fledged knights would have that sort of freedom to just head off on something like that at their discretion. I don't know how much personal time Jedi actually got, but I'd imagine most of them probably have pretty full schedules handed down to them from the council.
As for palpatine, your guess is as good as mine. For all we know things went off exactly as he planned, and maybe he sent Anakin the visions of his mother being in danger and engineered for her to be taken by the tuskens to nudge him further towards the dark side. (Total speculation on my part, wouldn't be surprised if that was the case though)
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