K.L.
This clingyness that your child is exhibiting has nothing whatsoever to do with your mother-in-law's behavior towards her. Someone cannot make or cause your child to have separation anxiety - and since you described your child as having been that way since birth, it is more likely that this is just a part of your childs personality at this point in her life.
I'm a child psychologist, and when dealing with very young children and infants, we use what I will call a "personality scale" (otherwise known as attachment theory) when describing the temprament of an infant. There are four categories in which all infants fall into somewhere: secure, anxious resistant, anxious avoidant, and disorganized attachment. Your child's behaviors and personality fall perfectly within the anxious resistant category : a child with an anxious-resistant attachment style is anxious of exploration and of strangers, even when the parent is present. When the mother departs, the child is extremely distressed. The child may be ambivalent when she returns - seeking to remain close to the parent but may be resentful or resistant when the parent initiates attention. 8 months of age is also a prime time period for seperation anxiety to start rearing its ugly head - and, unfortunately, this stage paired with your child's personality, makes a very difficult situation. But know that what is going on with your child has NOTHING TO DO with your mother in law. In fact, it may be in the child's best interest that your mother in law and other family/friends be around your child more often in order to facilitate her becoming more comfortable without mommy.
Your daughter needs to be around other children, taken to the park to see how other children relate to each other, and spend time with other family members without you holding her or comforting her. Have her play with other children near to her age, and keep within eyeshot but do not comfort or allow her to stick to you like glue.
I could go on and on here, but IM afraid this post is already too long. Please contact me for more specific information and ways to deal with your childs difficult time.