Divorce is a massive deal for an LDS family. I can only imagine how bad things were in that family for her to get to the point of filing.
We were shunned when my parents separated. I remember, distinctly, one young mother refusing to let me touch her baby, like it was 'catching'. The whole religion is structured around the perfection of the nuclear family, and when it goes wrong... let's just say a lot of judgement gets thrown around.
And, what most people don't realise about Mormons is that they marry for 'time and all eternity'. If someone loses a partner to death, they can remarry, but for a woman, that marriage can't be performed in the Temple and won't be recognised in the afterlife, whereas a man can have as many marriages in the Temple as he likes if he's a widower, and they all count, because polygamy still exists in the mainstream church, just after death.
The only way for a woman to be able to remarry and have it 'count' is to be granted a temple divorce by the church, and this is done rarely. You need a really, really good reason. It's an intrusive, courtlike process. Basically, your husband has to do something worthy of excommunication.
Basically, tl;dr, divorce is a massive deal, and just the loss of face from a civil divorce might be enough to trigger an abusive spouse.
My opinion, and experiences, only, but the Church is pretty open about the central pivot of family, it's why they're obsessed with genealogy, and their Proclamation to the World on the family is easily Googlable.