In a way, Tasha Yar's fate actually worked out really well for the series
I don't know whether this is an unpopular opinion or not but I actually think that the way Tasha Yar died gave the show much higher stakes throughout it's entire run. Here is the chief security officer, main bridge crew, tragic back story, potential love interest for the robot character just slapped down by the monster of the week. It made all the subsequent dangerous situations seem much more dire because "they were willing to kill off someone in the main cast". I also think that Yesterday's Enterprise was an awesome send off for that character that let them have a heroic ending for her after all.
It was a shame because I think Denise Crosby could have been awesome as a recurring character and in my opinion, we didn't get a great strong female character in the main cast (until DS9 which is an embarrassment of riches in that department). But I maintain that casually killing off Tasha Yar made my first watchthrough of TNG much more exciting.
I don't however like the additional stretch of her half-romulan daughter. It's pretty soap-opera-ish in my opinion and tarnishes the heroic sacrifice of her character.
They didn't want to fire her, but she did want to quit. She wasn't happy with the direction they were taking her character. I wouldn't be surprised if she also had issues with the same guy McFadden did. Jadzia was killed off because Berman wouldn't let Farrell switch to being a recurring rather than a regular, which may be what you're thinking of.