Your Husband needs to correct 'his' behavior.
It's not fair, putting that on your daughter's shoulder's to be responsible for. It's a heavy 'burden' for a child to carry around. In other words, your girl is hearing/seeing 'excuses' for her Dad's behavior....but not her's. She has no recourse.
In the long run....when she is a Teen... the manner of your Husband will not bode well for her... and will create more conflicts and 'secrets' and her not trusting him, lack of communication, and creating her views of what 'men' are and what she will in turn look for in boys, for better or for worse.
You NEED to think about this.
Yes, your husband loves his girls... but his 'short temper' is not good for anyone. Especially girls. He needs to take a long hard look at that....for their future.
*Adding this: my daughter is also 6 years old... sometimes my Hubby is a bit 'stronger' in how he 'scolds' my girl (he's not mean or loud/aggressive), but he's more 'manly' about it. Anyway, my girl is sensitive/smart/wise too... and she'll cry. So what I do, is talk with her- I tell her "I know Papa hurt your feelings.... I know you didn't mean to do that... let's go and talk to Papa about it..." (and then I 'practice' with my girl about what she can tell him)...then we go and talk to my Hubby, and we sit down and I say- "Papa, she would like to talk with you....she's sad..." and then my girl will say "Papa you hurt my feelings...I didn't mean to do anything wrong... it was a mistake. You took me the wrong way, it's not what happened..." And then, my girl will explain what happened... and then my Hubby will APOLOGIZE to her for 'wronging' her... and then they hug and my Hubby will correct himself and explain that "Sometimes grown ups make mistakes too...." AND, for me, this is a 'lesson' for both of them... for a Dad in learning how to approach his daughter, and for his daughter in LEARNING she can go to her Dad for anything and tell him how she feels AND THAT, he will HEAR her and RESPECT her, likewise. It's very important for a child, and for a parent to say 'sorry' too.
The thing is, it's not only kids who have to be "accountable" for their actions/words... parents have to be accountable to THEM too. Kids learn by this. And they learn problem-solving this way too, and TRUST of their Parents.
Good luck,
Susan