My cousin keeps asking to come to my ultrasounds...Was my response too harsh?

First, I know she wants to come out of love and excitement which my husband and I both appreciate. We are very close and she is like my sister. I let her know we would be finding out the sex of the baby in a few weeks and she blatantly asked, "Can I come?" I was a little taken aback at how direct it was and I was not sure if she meant to the ultrasound or to the small gender reveal party we are having after for immediate family. I let her know that if she meant the gender reveal party then we would absolutely love to have her. I tried as gently as possible to let her down about the ultrasound and said, "I'll have to speak with Brad (husband) about it as I think it might be something the two of us want to experience, privately. I hope that does not offend you."

She was polite back and said, "yeah, I understand. It's not a big deal."

I have a feeling it IS a big deal to her though. Do you believe I was rude or out of line? Could I have handled it better?