You have a great qualitative purpose here but your research questions

 
You have a great qualitative purpose here but your research questions is phrased like a quanitative question. Asking about a “relationship” implies that two variables can be measured and associated by statistical analysis. Here those would be your mental health factors and domestic violence. For qualitative work, you might ask those who have been violent toward others to describe their mental health and focus on experiences during childhood or throughout the lifespan that may shed light on the behavior.