She is a new Muslim and is complaining about her husband

I am a woman, who al-Hamdulillah, Allah guided to the straight path of Islam.
I do my best to follow Allahs deen, but I need some advise on some problems in relation to my husband.
I must tell you that the situation in our marriage is somewhat strained. Only a few months ago I came to the point when I asked my husband for a divorce because he neglected his Salaat even though he had been told about his duties, and he also had developed a bad habit of threatening with divorce and actually throwing me out of the house when he lost his temper. But when he realised that I was actually going to leave him, he repented and changed his ways, so I withdrew my question and returned. But there is still some tension between us. This is mostly due to the fact that as it is today, my husbands eeman is weaker than mine. I do not think I am perfect, and I know I also make mistakes. But I constantly see my husband doing things that are wrong (both things haram and makruh), and I cannot restrain myself and not speak to him about it. This is for example like using bad language in front of our daughter, or biting and kissing her in places where she should rather learn shyness, etc. When I tell him that it is not good to do these things, and sometimes I am able to give evidence from Qur'an and Sunna, he will either say that he knows this, and then continue with what he is doing, or become angry and tell me to mind my own business. This is a source of irritation for both me and my husband, and we are losing patience with each other. My question is: What is my test from Allah here? Is it not my duty to inform or remind him of what is right when I know it? Or should I be patient with him and wait till he finds out for himself, because he has started to read Islamic books. The reason I need some advise on this issue, is that my husband is getting quite annoyed with these reminders, and I am losing patience and becoming angry when he doesen't listen. Please try to give some advise, and please show the evidence from Qur'an or Sunnah that you lay to ground for your advise.