I think you should talk to other moms face to face about this. It is pretty common. Maybe you need to tell your Dr. that you are very concerned about this and you expect him to take it seriously. After saying all that, I honestly wouldn't be overly concerned. I don't know your whole situation, but the fact is you have met and loved your first, including holding him/her in your hugs and kissing. This new one hasn't come out to meet you yet, and is only seen in your mind, although you know the baby is in there. In my case, I not only had to contend with that, but I'd had a couple of miscarriages very early in the term. One was between my first and my second, so with that track record I was mentally distancing myself not to care too much. In fact, I started spotting & small clumps came out around 12 weeks. I thought all was lost until I decided to go in for the scheduled checkup (they'd thought I'd lost her too) and found a strong heartbeat. They never did find the reason for the bleeding, but found that there was definitely some inside. I now have a beautiful, healthy 4 year old to go with her older brother. In fact, her brother had problems during birth, too, and was born with forceps, so they had to do some stuff quickly when he came out. He's also very healthy. One of my problems is that I felt we'd dodged the bullet with him; would we be so lucky again?
So, you could be experiencing hormonal issues big time, she/he just may not feel like a real person yet and face it, life changes a bit after each baby. I don't know what is exactly normal, but you are not feeling anything you "shouldn't" feel. We are all different, and every birth, even in same families, is different. Enjoy your pregnancy and know that you'll fall in love with your new bundle, even if you are exhausted at first and having to deal with hormones for awhile. If you still feel there's an issue at your 6 week checkup, or it really concerns you before then, make sure your doctor listens. What's most important is that you feel good and can cope well. Baby will feel happier, too. Oh, and sleep is really a huge key.
Good luck to you. You'll make it just fine.