I think a few of us can relate to your feelings.It seems a particularly common issue especially for dads with daughters, especially if the mum is hostile.
How old is your SD? How long with dp and does the ex have a partner?
I found that dp coped with his ex's rants far better than me.My reasoning being , he had married her and was used to it.It made him v unhappy so their marriage ended.Weekly rants were in, his mind a massive improvement however I didn't have a hostile relationship with my ex so it was alien and upsetting to me.I guess in some ways I must have had a more fortunate life as I hadn't been exposed to such unreasonableness before.
Someone a while ago posted a link to SD being hostile, via proxy, this is really informative.I sent it to DH, he hasn't really commented but I know it has gone in.It hard for him to accept his daughter may be capable of such unpleasant behaviour.
Even if DH 'gets it' he is however limited to what he can do.He has a fear of correcting his daughter as he doesn't get to see her much.He can't moderate his ex's behaviour, 3 husband's have tried that! So he is a bit powerless and I suspect your dp feels the same.All he can say is 'try to brush it off' as he doesn't have any other alternatives to fix it.
What would you like your dp to do or say? Is it to validate your feelings? If so try the asking him for this explicitly.
The reason I ask how old SD is because if she is young you do need to factor in if you can live like this for years.You can't be sure it will get any better, ours did to a certain degree BUT it's still not ideal and SD is now at Uni.