It must be difficult, especially as you live apart. Write a love letter. I know it's cheesy, but pregnant women are hormonal and I'm sure reading this sort of thing in her own private space will have her feeling good (in a teary way!)
Use the letter as an opportunity to reassure her you love her and your baby. Tell her you're here for her but that you understand she's tired and feeling sick. Say you're sorry you can't go through that part with her, but that you're always on hand if she wants to moan (let her if she wants to...it's part of the deal!)
Say it's ok if she wants some personal space but that you'd love to attend the ante-natal appointments/scans so you can be there for her and understand this amazing process. Say all the positive bits you've said above.
I'm sure as hell you're feeling hurt, confused and angry that you're being excluded - and I totally respect that. It's hard for a man because it's all taken out of your control.
While you're just desperate to be involved and you're well-meaning, if you're going on and on about it, from her perspective it'll just seem like harrassment and she'll get defensive. Both of you have valid points of view but one of you has got to give, and I'd say it should be you (sorry!)
Once you've sent the letter, wait for her to get in touch.
It sounds as though the pregnancy is a huge shock for her. She's trying to get her head round it. I totally understand what she said. She wants to be as happy as you and she's feeling bad that she isn't. She was trying to take your feelings into consideration while trying to come to terms with her own. It sounds like she definitely loves you but she needs to do her own thing at the moment. My suggestion would be to let her.
There are around 40 weeks of pregnancy, and the first few months are pretty uneventful (from a bump and baby persepctive) so I'd say bide you're time, be on-hand but not in her face, and she'll come round eventually.
Good luck!