If anything, Joanna’s approval could have read as a mark in her favour - a sign that he chose well when he selected his wife

Hi, good to hear from you again, I’m happy to help! Please, you’re not a bother! I’m excited for this project!

Hi Lannisanta! Sorry my answer is late!

JOANNA

Loyal

Ambitious

(relatively) Openminded

TYWIN

Proud

Devoted

63. INT. - FATHER'S CHAMBER Father and Vincent stand inches apart. FATHER Do you think it was easy for me? You can't know the price I paid... [...] Vincent rips free of Father [...]. Each word is a body blow. FATHER For years afterward, I could see her face... sometimes, when I pass through the Chamber of the Winds, I can hear it still... the screaming, and the... the sound you made as you... tore your way into the world. Vincent's [...] sick with horror. VINCENT Stop it!  Stop it! FATHER You have to hear.

Tywin and Joanna were married for about 10 years. (It’s unclear whether they had already celebrated their 10th wedding anniversary before Joanna’s death, but I like to think they did.) 

Hello! Are you asking, did GRRM deliberately set up a parallel between Elizabeth of York / Henry VII? Not to my knowledge. 

Based on his responses to interview questions in 2012, I don’t believe GRRM had given much thought to Tywin & Joanna at all prior to The World of Ice and Fire. GRRM describes himself as a “gardener” type of writer rather than an “architect” type of writer, so, paraphrasing his own words, he doesn’t name a mountain range until he crosses it. 

I don’t think GRRM thought very much about Tywin & Joanna’s relationship until he got to it in the World Book, and even then, the book’s emphasis on male characters means it’s all mostly about Tywin, with very little information about Joanna. I don’t think you could make a strong case that Joanna Lannister in the text parallels any particular historical figure because GRRM hasn’t really bothered to write Joanna in the text. Much of the discussion about Joanna Lannister is fanon, aside from whether or not she was raped (thank you so much, GRRM). It’s fanon that I will literally fight people to the death over, but it’s still ~80% fanon. 

The story of Man’s Beloved Wife Dies, Man Becomes Hard(er) And Cruel(er) isn’t exactly rare. That describes Henry VII in this post, Tywin Lannister, the origin story for the beast in La Belle et La Bete (2014), and the origin story for Dracula in Dracula Untold. 

So no, I don’t think GRRM meant for Tywin’s relationship with his wife to parallel any famous historical relationship. Not when GRRM didn’t bother to fully flesh out half the relationship. (I would be more than happy to be proven wrong here, Mr. Martin!)

But were you asking instead, does Elizabeth of York / Henry Tudor remind me, personally, of Tywin/Joanna? 

Because my answer to that is, sort of? Not really? 

Both men obviously loved their wives very much, and I imagine there are similarities in how Henry VII and Tywin reacted to their wives deaths (click here), but their stories are very different. I don’t think Henry Tudor murdered two whole Houses at 19, for example. And I don’t think Joanna Lannister was a nice person, whereas this post describes Elizabeth of York as a good and kind person. 

A World of Ice and Fire app

Some things to note:

"As a maiden, she served as a companion to Princess Rhaella": if you think Aerys had sex with child!Joanna, you're kidding yourself.

"acquainted with the future Princess of Dorne": the Unnamed Princess of Dorne was not yet the ruler of Dorne during the War of the Ninepenny Kings.