It could be this simple. Perhaps Gerard took advantage of Allison not being home to collect something and his mistress accompanied him - sort of thing you would do when you are in love. Perhaps even Allison came home and found them in a compromising position.
Allison would feel annoyed " I have told you not to bring that woman here" , an argument ensues, perhaps a physical one between Allison and the mistress, Gerard tries to pull them apart and gets involved, the mistress challenges him - her or me, and the situation accelerates and a pillow or hands are used to suffocate or strangle Allison, and then the deception begins.
Just on the children, we know they were at a sleepover and they live very close to the school, at 7.30 or before school wouldn't have been opened and perhaps they had no idea how to sign in for OHC or it wsn't opened yet, so who ever it is says, "Look Mummy is still home , want to go say good morning, perhaps they forgot something, they run and are confronted by Daddy and/or the solicitor and the reasonable question is where is Mummy? he answers the question strangely and gets them out of the house quickly. If the police arrive during this time, it could look really strange, in particular if he says the girls were at home all night and one of them contradicts him.
Also the dynamics of having three daughter, means one will be seen by her siblings to be Daddy's favourite, quite an important role in a family dynamic, protects Daddy from Mummy, loves him better then Mummy but not ion the same way as the mistress. Too many woman in your life Gerard, you can't keep all of them happy.
