There must be some, but I’m drawing a total blank. Seems like it would be good lyric fodder for metal 
Ding Dong, The Witch Is Dead 
Herman’s Hermits Mother-In-Law
Harry Champion. Harry Champion - Im Getting Ready For My Mother In Law - YouTube
Which was a cover of the original Ernie K-Doe song:
[nitpick]Mothers-in-law[/nitpick]
sorry
K-Doe even opened a bar by that name - Ernie K-Doe Mother-in-Law Lounge, which only recently closed (I heard Kermit Ruffins bought the place).
I know no one cares, but there’s lots of songs in Hindi. The only reason I wanted to post was to provide the lyrics to one of them:
“Sas meri tha badi kapati bina gaal na bole
Ni main sas kutni,
Kutni sanduk a ole,”
Essentially,
“My mother-in-law is such a bitch, she can’t talk without swearing at me
I’m going to beat the crap out of her,
Out behind the shed.”
Enjoy. 
Not really ‘about’ the MIL, but…
Dr Hook and the Medicine Show - Sylvia’s Mother
The Proclaimers: “Don’t Turn Out Like Your Mother” ?
Bob Rivers’s “The Twelve Pains of Christmas” includes a mother-in-law psychodrama at the sixth day (and ramping up in the repeats through the next six), including “She’s a witch…I hate her!”
You DO know that there’s now an awesome book about Ernie K-Doe? By my old friend Ben Sandmel:
Enjoy!
There’s also “Mother-In-Law Blues”, by Junior Parker, covered also by Johnny Winter and many others.
I know she heard me callin’, she looked back and waved her hand
I know she heard me callin’, she looked back and waved her hand
I could hear her tell her mother, “That’s one no good man!”*
No, thank you 
The Squirrel Nut Zippers did a little old-timey rag song called “Little Mother-In-Law” but there doesn’t seem to be a clip of it online.
“My old lady’s / got the cutest little mother-in-law/
she’s just a little bit crazy / she’s the sweetest mom you ever did saw”
There was a British Armed Forces song called “How I love her, how I love her, how I love my Mother in Law”.
Obviously totally derogeratory, might be versions on you tube maybe.
You Shit Me to Tears by The Tenants
Not ovious from the song title, but one of the all-time best Mother-in-Law songs is Situation Vacant from the album Something Else by The Kinks.
Oh yeah! Good one!