When he kicked the dog you should have called the police and had him up on a charge of causing an animal to suffer unnecessarily contrary to the Animal Welfare Act 2006.
As it is you could consider reporting him to the rescue centre who may press charges against him, and who may seek to rehome the poor defenceless creature with people who know the importance of being especially caring towards animals who've previously experienced ill treatment from humans.
When/if he apologises, tell him his apology is not accepted and you are no longer prepared to remain in a relationship with a particularly pathetic apology for a man. Also tell him that you want him to leave and find other accomodation, preferably today - don't hesitate to call the police and have him removed if he kicks off.
Are you married to this abusive cretin? If so, source a SHL of the rottweiler persuasion and let him/her give him a taste of his own medicine by kicking him in the wallet where it hurts.
If all of the capital that went into the purchase of the house is yours, seek to obtain a division of any jointly held assets whereby you can buy him out or buy another property and don't give any thought to whether this means he'll have to rent as his problems are his to own and yours to disown.
As for your worry that he will be less than nurturing to your dd when/if she spends time alone with him after you've split, you need to face that fear head on and realise that she will let you know if she's unhappy when she spends time with him at which point you can take steps to ensure that her contact with him is supervised or doesn't extend to overnight stays.
In any event, I suspect your dd is already damaged by the 7 years she's spent under the same roof as her turd of a df and it's incumbent on you to ensure that both she and the poor dog don't spend a day longer than necessary with a temperamental twunt in your home.
If you have a spare bedroom I sincerely hope you moved into it last night, or bunked in with your dd and the dog, and that you won't be sharing a bed with the twunt again.