How much must I cover when breastfeeding?

What is the position on modest breastfeeding in front of one's non-Muslim family members, including a mother, stepfather and stepsister? It is done with a minimum of exposure (only a small possibility of some skin being visible when the baby is taken off or put on the breast). Is this improper? Given that my baby breastfeeds often and sometimes for extended periods of time, as I feel is the baby's right, during long family visits, it becomes impractical to leave the room for every feeding. This is a follow up to the question on women covering in front of corrupt women. 

The sister should consider wearing the headcovering popularly known as "khimar." This is a cape-style hood that pulls over an underscarf. It comes in varying lengths: wrist, hip, knee, and calf length. When the baby needs to nurse in a semi-public or public situation, it will be very easy for her to prepare herself and nurse him under there without ever revealing any part of her body at all.

Khimars are made out of lightweight polyester -- much lighter than a receiving blanket, which some people use to nurse. Because it is worn over her head, she does not have to worry about it slipping off or the baby kicking it off, as he would with a blanket. If the sister doesn't want to wear this style of headcover all the time, she can keep one rolled up in her bag, and simply slip it on over her headscarf when the baby needs to nurse. The fabric is very easy to care for, so if the baby spits up on it, she can just toss it in the washer. 

If she is in a situation where she isn't covering her hair, she can loosen the seams of the khimar and slip it over her neck, like the cape one puts on when they are getting their hair done at a salon. If she wants to use a receiving blanket or regular scarf, she can buy a bag of plastic laundry clips at a dollar store and clip it to her shoulder before nursing the baby. She could also use hijab pins to pin a scarf to her shoulder.

And Allah knows best