In the second situation where the child will only settle to sleep in their parent's bed you could try moving your child's bed or cot into your own room. (rollercoaster.ie)
Often this phrase is to do with baby not sleeping at night but often it can be when baby won't settle to sleep for his daytime naps. (rachelsbabies.com)
It's what every new and most probably exhausted parent desires - a baby that will settle to sleep easily at night, and learn to sleep through the night. (bounty.com)