It is great to chat to you again and I can hear how much pain this is causing you and I am so very sorry, that is so very hurtful for your stepmother to say that she dislikes you and your sister and also says the same for your mother and aunt, it does seem like from what you have explained here that she is really trying to make a line from your dad's "old family" to his "new family" with her. She does sound like she is extremely insecure about the relationship with any member of his past life, including you and your sister. Can I suggest that perhaps you have a chat to your dad to ask him why he didn't take you up on your offer to pick them up from the airport?. Tell him that you saw it as an opportunity to see him and you miss and love him, not to mention the cost savings, that is just didn't make sense, that you too thought it was a good idea then when discussed with your step mother the offer was rejected.
I can see why perhaps she had declined the offer, to assert her power over your father, she probably feels she has little control and feels insecure so these are the times she can gain control and feel him take her side, is it right , no and does it hurt, yes but I think for some reason she is hurting too and feeling very insecure. Only she will be able to shed light on this.
I am so pleased you have spoken to your dad, he too is probably so very confused and hurt too and really doesn't know how to manage this situation either, he does love you and the fact he said he will call you weekly is wonderful, but you want your dad in your life and I can hear how much this is hurting you.
Perhaps a call to a really great place called Life Supports on 1300 750 297, they deal with all sorts of family issues and would be a great place to chat to a professional and to get some advice on how to manage this and how you can encourage your dad and also try to get your step mother on board with acceptance of his past family and that you do exsist and you are most surely not going anywhere.
I am not sure that I am helping here but I am so very sorry that things are like this for you and your family, I can hear how much you love your dad and that is so wonderful.
Hugs to you london1298