Agreed on the second point. There's certainly evidence that looser divorce laws allow people to leave unhappy marriages [1], though there's also evidence that these laws made marriage less stable and harmed children, so there are trade-offs [2, but see also 3].

I'm less sure of evidence that cultural taboos have the same effect. Here's some correlational work across countries on divorce norms and gender equality within marriage; this doesn't specifically address violence, though, and it doesn't control for other aspects of culture which probably covary with attitudes to divorce [4].

[1] Stevenson, B. and Wolfers, J., 2006. Bargaining in the shadow of the law: Divorce laws and family distress. The Quarterly Journal of Economics, 121(1), pp.267-288.

[2] Gruber, J., 2004. Is making divorce easier bad for children? The long-run implications of unilateral divorce. Journal of Labor Economics, 22(4), pp.799-833.

[3] Wolfers, J., 2006. Did unilateral divorce laws raise divorce rates? A reconciliation and new results. American Economic Review, 96(5), pp.1802-1820.

[4] Yodanis, C., 2005. Divorce culture and marital gender equality: A cross-national study. Gender & society, 19(5), pp.644-659.