Hi A.,
I'm so sorry that you're having these issues with your daughter. I also have a 3-month old son and a 3 year old daughter and it sounds to me like your daughter may have reflux (as my son does). Often babies with bad reflux can't lie down flat and have trouble eating b/c of the constant discomfort and will cry and scream because of it.
I'm a little concerned that your pediatrician is taking things in stride seemingly. This does not sound like normal behavior to me. Is there anyway you can get a second opinion? Does she scream when eating too? Curve her back in pain? These are all signs of reflux, but even from what you wrote that is what it sounds like to me. Plus, if she is not really eating, she could be hungry. Curing the reflux will help. She could also have a food allergy, which is causing her discomfort. Their stomachs and digestive systems are so immature at this stage.
There are many natural reflux remedies out there (like Colic Calm, which you can find at CVS or online). It didn't work for us, but others swear by it. You could try it out and see if it makes a difference. We ended up going to Zantac, which helped for a while and now Prilosec, which has made a difference. You could also start out with a gripe water to see if that calms things down a bit. She could just be in so much discomfort that she doesn't want to eat. Have you also tried different formulas? Either soy or nutramagen (which is the easiest on the belly)?
This isn't related to a possible reflux problem, but because you mentioned she likes sleeping by your dog, have you tried swaddling her? She may just like the comfort and warmth and swaddling can help. Also, see if inclining the mattress where she sleeps a bit (no more than 30 degrees) to see if that helps. She may also just be the type of baby who likes to be held and kept close while sleeping, but needing to sleep on the stomach sounds like reflux or colic. Being alone in a crib can be lonely for a baby, too. Often the open space bothers them as they like to be in confined spaces.
Hope this helps and good luck!