I do agree that the daughters behaviour is deliberate, rather than just plain rude.
However, having been in the situation from all sides - as the stepchild (x2), dealing with the non relationship of my young adult DCs with their DFs partner and their relationship with my DP it isn't always straightforward.
How old are his daughters? Do any of them live with him? If you got together quite soon after his wife left they could still have been grieving for the loss of their family (my DD has used that phrase) and not be comfortable with someone else especially if you have kids. Not that their behaviour is remotely acceptable, but they may feel pushed out and unwanted. You also don't know what has been said to them about your relationship with their father, especially as his marriage breakdown was (I assume) acrimonious with OM involved. Do they have a good relationship with their DM?
I would be cautious about getting him to speak to them. Men aren't the most tactful and if he says something like 'ellie isn't happy about the way you speak to her and I'm not putting up with it', it could just make everything worse.
I just think there is more to this from their side - yes, the behaviour is rude and bullying - but it's not necessarily their normal behaviour. If your partner isn't like this - why would his daughters have been brought up in that way? I would be more inclined to stay out of their way for a bit and see if things calm down if they realise you are not trying to take their father away.
Having a relationship where there are young adult/teenage DCs is not easy. Confrontation makes it more polarised. If this relationship is important to you then try and work through it.