One thing that might help is if this woman and your brother have a little more respect for the girls' needs. I would be frustrated too if my dad was on the phone with a girlfriend during bedtime routine every night. The girls need their dad at that time of day, especially if they are all still grieving. That would be a good time for him to listen to their woes and hold them when they miss their mommy. Maybe that's what they want and they feel that this woman is intruding on that.
Next, your brother needs to make it clear to the girls that he still loves their mother very much. He needs to explain that dating this other woman sometimes helps to ease his loneliness. He shouldn't tell them it helps with the pain he still feels because that could make them think he's trying to replace their mom emotionally. He should have an in depth discussion with his oldest daughter about the nature of adult relationships emotionally speaking. He should explain in great detail how much he loves her mom even though it will be very hard for him to speak about. She needs to know that her mom's memory will live on. Maybe he could say something like their bond of love with her has not been broken and reaches into Heaven now. He could explain that grown-ups also need a bond of some sort here on Earth. We need that kind word or touch, we need to know there is always someone we can unburden ourselves to, we need to have that counterpart that we can rely on to provide comfort and caring. This is doubly true for someone like him. He has been deprived of the woman that was his partner and the mother of his girls. It's very hard for a man to go through something like that. He needs some female companionship within guidelines that are respectful to his girls and their feelings about their mother of course. He has to find a way to convey these ideas to the girls.
He should also make a pact with them. On their side, they will give anyone new a fair chance and get to know them before they make judgments and on his part he pledges to listen to their feeings about anyone new with an open mind. This lets them know that if they really, truly can't stand someone, he will listen and think about the problem. Hopefully he would decide that he shouldn't bring someone like that into their lives, but he shouldn't make promises like that because that's a situation that could get out of hand.
Anyways, I hope this helps. We all know what it is to grieve. The kids just need more time.