How do I protect my 5 year old?

I do want to cry right now out of frustration, but my main issue that I feel unable to resolve is my childish husbands rollercoaster of an attitude with my daughter.  A little background, he has two children from a previous marriage he is unable to have consistent contact with and hasn't seen in over a year.  Me and my daughter have moved to Australia with him and now are expecting another child due in a month. 

This evening my baby made an insensitive comment and while it was something she needed to apologize for and understand why it was wrong to say, his over the top reaction to a child saying something childish and letting his anger last for hours is really hurting my heart for her.  He said such things as she needs to go back to her dad and he needs to start paying for her, he has two children in America and he wont stand being around someone that disrespects him... ect.  A while later he asks my daughter if she loves him.  It takes her awhile to answer and when she does she says no, oh goodness this sets him off again and he amps it up to "she hates me, that's it I'll have nothing to do with her" then about 5 minutes after that she gives him a hug and says she was just messing with him, and he's sweetness and light, like none of his ugliness ever happened... like he had forgotten just how "done" with her he was, and he's making all these plans with her to do fun things on the weekend.  Then not 10 minutes later we're watching a movie, he gets up and says goodnight, goes into the bedroom and closes the door. comes back out a minute later to turn the movie off no one was really watching and Cheyenne makes the innocent comment that now he can go back to bed, (I knew where she was coming from and it was not an impertinent comment, it's how she expresses herself and she was in her mind being nice) well he took that and ran with it repeating all his rants from before, and adding in new ones about not having some 5 year old tell him when to go to bed, and how he's not supporting someone who hates him. blah blah.   I'm a little dumbfounded, 1 he had just said goodnight and made like he was going to bed.  2 Cheyenne and he JUST had a little moment or so I thought where she said I do love you and he was telling her how great she was. 

His anger and inability to show self control in the middle of the silliness of children make me fear for my daughter to be around him alone.  My stomach is actually a little knotted up right now.  Yes she will run to him after his tantrum and hug him, she's a child she forgives easily and even when she makes a mistake, there's really no malice in her.  But I'm older, I see the wishy washy way he deals with her and even when she's running to him to play and things seem okay.  I am all tight inside wanting to keep her close to me and safe. 

Any problem he has is always boiled down to it being my daughters fault for making him feel or think or do one thing or another.  She repeated something she heard me and his father say about Tim acting childish and she bursts in the room and blurted out what we had said.  Now I can't get too mad at a child repeating what they hear an adult say, I feel I have to take responsibility first.  Tim on the other hand berated, shouted and went really overboard with his angry outburst to the point of coming home today slamming things, knocking over stuff and just overall letting everyone know he is upset.  Over what she said last night.   I don't subscribe to the view that you hold grudges over children.

I just really want to cry, because later once he's calmed down he'll be so open to understanding and apologetic and admitting to his over reaction.  Then later, whenever he feels he's been slighted by my child he'll fly into another tantrum. 

And as a side note, he has really idolized or put on a pedestal his two children he can't see right now, and to a large extent I can understand, it's gotta be hard being away from your blood like that.  But what he does that I don't like at all is think that any mischievous or misunderstood, less than pristine behavior from my daughter is 1 a personal affront to him and maliciously meant to undermine him  or 2 some foreign behavior that his children would never display.  they'd never talk back they'd never have to have something repeated a few times before they do as they're told... and that constant comparing tears my heart up to have my daughter subjected to that stupidity.  I just don't know what to do.