Okay so some of you may be aware of the series known as Evolve, back in 2001, Bandai premiered a series of animated shorts to accompany various model kits. The shorts all feature a starring Gundam from one of the various anime series in miniature side stories. In most of the shorts, the goal was to show a Gundam rendered in high quality CGI.
Originally touted as the finale of the Evolve series, this installment was again directed by Ryukow Masuo and features a story by Yoshiyuki Tomino. This segment poses an alternate scenario to Quess' fate in the movie Char's Counterattack. Instead of being killed by Chan Agi, Quess is able to understand Amuro and Hathaway and sets off to save Hathaway. This change in tone probably has a lot to do with Tomino's own change from the time he did Turn A Gundam and onward. The angry Tomino from 1988 certainly wouldn't have given Quess a happy ending, but the Tomino of 2003 is a different man.
And here's the summary in brief from MAHQ:
UC 0093, Quess Paraya uses her mobile armor Alpha Azieru to attack Hathaway Noa's Jegan. Amuro senses Quess and speeds over to her location in the Nu Gundam. Quess says she hates everyone, and Amuro asks her what she did to Hathaway. He asks how she could do that to a friend, and she replies that Hathaway isn't her friend. Amuro tells her she should consider Hathaway's feelings, and she tells him he's always getting in her way and talking big. Quess fires at Amuro and unleashes her funnels, and Amuro dodges the attack and deploys his own funnels. Amuro uses his funnels to create barrier around the Alpha Azieru. Quess tries to break out, and he tells her that with her careless attacks she could end up killing her own family. Quess tells him she isn't that stupid, and Hathaway's voice tells her not to be angry. Quess calms down and calls out for Hathaway. Amuro tells her that Hathaway is in the direction of the sun, and she can save him if she wishes. Quess detaches parts of the Alpha Azieru and heads to Hathaway's position.