What made me get back together is the simple fact that Ashley is a great character, and a lot of people don't see this or don't want to. I see a lot of Ashley hate on these forums and elsewhere, and it mostly consists of her being a racist ******, which she really isn't if one would take the time to explore her character.
Ashley is a dedicated soldier and human being, striving for the best and hindered by her past, and probably by the fact that she's a female soldier who can hold her own against any male but is being held back by sexism from her superiors. As she says ' as a Williams you have to be better than the rest,(to make up for Shanxi'). It's where her grandfather surrendered in the First Contact War to the Turians. An army consisting of humans being defeated by aliens.
It has made her very driven and at times a bit blunt, but she does care a lot for the people close to her. She mentions the importance of her family, how she helped raising her sisters in the absence of her father and this is evidenced in ME3 with her supporting her sister who lost her husband.
She is by no means xenophobic or racist, she befriends several alien squad members and during Virmire she teams up with Salarians respecting their skill and tenacity.
If you cheat on her with Tali in ME2, she accepts it more or less saying that Tali always felt like a sister to her.
Apart from all this, she hates Cerberus with good reason, as they are a terrorist organisation (which was made very apparent in ME1) that perform inhumane experiments as shown in ME3. She has very good reason to doubt Shepard there. The irony here is that she denounces an organisation that is known for being racist, while she is being accused of that by a lot of people.
The scene on Horizon on itself isn't that bad if it weren't for the fact that there is no way to reconciliate after.
Long story short, Ash is worth it.