Just a quick reminder to the thread... I think everyone is being very gentle and aware, but do let's keep the focus on the OP and her situation and not get side tracked into a discussion of the personality or behavior of the mom or the role of individual members in that family. There's a lot of second hand/third hand information and it's impossible to tell what is actually going on.
It could be a mental health concern (I've had PPD and PTSD following an unplanned c/s and despite advanced degrees and a full "understanding" of PPD I wasn't the one to "turn myself in"... I was fortunate enough to have a DH and a family dr who saw the signs and got me the help I needed but most assuredly didn't "want" or feel was at all applicable "to me" at the time). Mothering Magazine has some wonderful articles about PPD and PPPsychosis, but even a gentle suggestion of a well known mental health disorder from a non-family member might not go over very well. :(
And it could be this family is following one of the (sadly, many) parenting philosophies that include scheduled feedings. There have been infant deaths and court cases and much heartbreak surrounding some of these philosophies, but the books are still widely available at mainstream bookstores and are even the corner stone of some church based parenting programs. If this family is following a specific philosophy, and especially if it is one that is encouraged by their church, then again... a suggestion that the philosophy is doing more harm than good for their infant may be taken the wrong way. However, you might approach the minister of their congregation if that is applicable here.
It's a very difficult situation because things like scheduled feeding or a lack of socially displayed maternal affection aren't "crimes". A call to the family doctor (or minister) about possible PPD/underfeeding might be more helpful than a call to CPS since, again, scheduled feedings and a mother who travels for business aren't crimes and while CPS may open a file they probably don't have the staff/time/budget to investigate this sort of report in any detail.
And outside that... can you spend more time with this family so you have first hand information and can, perhaps, lighten some of this family's "new baby" load? Model other parenting philosophies in a non-confrontational way? Perhaps suggest a visit to a local ICAN or SOLACE group (these also have online support forums, ICAN specifically surrounding cesarean birth and SOLACE for all different sorts of birth trauma)? Offer to go with her to a LLL meeting so she can see other breastfeeding moms and perhaps adjust her expectations along those lines? Drop off a mother care package (c/s is major surgery, Earth Mama Angel Baby makes a c/s recovery kit, or you could make one yourself with some Milk Maid tea, lotion for scar massage, maybe a soothing eye pillow with lavender oil or some bach rescue remedy spray), offer to bring over a complete meal or two, that sort of thing? And have your partner "hang out" with his best friend a bit more with conversations along these lines?
I never would have gotten the help I needed if it hadn't been for my DH basically telling my doctor at a PP visit that he was sure I had PPD. I could have killed him in that moment, and I was mortified that I wasn't "holding it all together"... that someone, anyone, could POSSIBLY think something was wrong. But I'm so thankful he did what he did. And he is under standing orders to turn me in again if I start down the PPD path again.
Good luck to you and your friend... no matter what, she is fortunate to have friends who care and worry about her!