Your own mental health is important, too. When considering your own needs, you aren’t being greedy or selfish. Being a better, healthier person makes you better towards others.
It concerns me that your wife is reluctant to consider mental health support. Hopefully this is just an initial fear that will fade over time, but maybe it isn’t. If she won’t help herself, you can’t have a positive family environment, and that will hurt your daughter, too.