No you're not. Your strongest objections ignore the obvious example of PCs, which in every edition of D&D since 2000, at least, can go from 1st to 10th level over the course of a couple of weeks of intense dungeoneering. Or less, even.
If the PCs can do it, the PC's mom can do it.
Note that I said "Something that takes
most non-adventuring wizards the best part of 50 years, often more. And that's starting when their brains are young - and asuming that the spells are accessible (whihc in the case of lichdom they normally aren't.)"
If there is a 35 year old woman who suddenly starts to learn spells and throw herself into mortal peril because she fears death (wait, what?), then she's going to be the centre of the town's gossip. Such a thing would have massive ripples in the surrounding world. (Set it up like that and it could possibly be done).
Heck, maybe the PC's mom was digging through dad's old things in the basement and came across some magic item that granted her some wish or miracle spells or something.
There's tons of ways to explain that that makes sense. You're just not willing to entertain the idea because you've fixed it in your mind that it's "impossible." For some reason.
And every last one of them is a DM case of Deus Ex Machina or takes a lot of foreshadowing to be met with anything other than eyerolling.
At this point, I honestly have to ask; why is this player so invested in keeping her character's mom in this static environment?
Just because turning the mother into a lich is utterly ridiculous doesn't mean it's a straight choice between the ridiculous and absolutely nothing. Plots that wouldn't be static but that would be fine include town politics, remarriage or affairs, joining cults (including good ones), death, debt, winnings (including betting on kids to succeed), etc. Even learning a little magic is fine.
You're running a false dichotomy.
Why is she so invested in, "this is my mom; this can't possibly be what my character thought of my mom all her life, but my mom was secretly something else."
1: Because the Lich example is ridiculous
2: Because it would involve every single interaction with the PC's mother and those she influenced needing to be re-evaluated. i.e. half the character's life would have just been arbitrarily retconned (seriously, you think every incident goes into the written backstory?)
Why not have a mom who was a doppleganger?
Genetics. (Unless you mean that the mom was a doppelganger who adopted the PC when the birth mother died in labour when it would be moving into odd territory, but not automatically eyerolled unlike the rest of your suggestions)
Why not have a mom who's a frog who was polymorphed and awakened by a kiss, but never told anyone? Why not have a mom who seems like the fantasy version of June Cleaver but who secretly sacrificed all the character's best friends to Orcus after she left town to increase her own power? Why not have a mom who turns into a horde of butterflies every night like a bizarre Ladyhawke?
Um... you are running a comedy game here with no attempt at immersion, right? Or possibly a parody?
NPCs can't keep secrets from the PCs now? Seriously; why not?
Not when the player knows a hell of a lot more about that character than the DM does. Now if the player and the DM agree the secret, and have it kept from the PC that's fine. If the DM wishes to re-write the core of the character, that's not collaborative. That's the DM throwing a bucket of paint.
Also secrets that don't change who the character is are fine. A secret that the character's mother was having an affair with the local lord wouldn't be one that would colour every single interaction she had. Even a secret that she became pregnant by him and the character is the lord's son (I'd run that one past the player, personally).
In the case of Anakin Skywalker, things weren't this way because all the player knew was that Luke's father was dead - there weren't an entire host of unwritten but still important interactions to revise. And as a player I'd have probably written the hook onto the sheet. "Father: Dead before he was born (or so he believes)."