I would evaluate this baby further - how was the labor/ delivery?  Head molding? Torticullos? Suck dysfunction, TT,  there is a reason why is doing what he is doing 
CST would be great for this situation/ lots of STS.  As far as her breasts are concerned:
I would have her pump on a comfortable setting, making sure the flange size is appropriate etc, no more than 15 min with gentle massage.  The bleeding will stop.  FYI-even though the blood isn't harmful to the baby just a tip : If there is blood -you can let the milk sit -the blood will settle to the bottom of the bottle and you can scoop out the milk on top and use that.
Good luck even though it is distressing, doesn't last long -I think perhaps small capillaries open up causing this frank red blood and then seal themselves off. I have seen it early postpartum and later if moms are pumping at too high a setting.

Maria Parlapiano RN IBCLC
Chatham, NJ

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