Your mother in law sounds like a bit of a nitwit, frankly.
I had a similar experience with my last: my mother in law was put out that I gave the little one to my beloved sister in law to hold when they were visiting. I'd had a very difficult surgical birth and was only just down on the ward from HDU, and in a lot of pain and really not up to family drama.
My sister in law is the named guardian of my children in my will, and the sole trustee of their trust funds. She is the person I most trust to act correctly in the world. I was so glad to see her kind face that evening when I was so upset and sore. I was more than happy to hand her the small one.
If we all carved up our family bonds according to 'blood' and 'not blood', well, that would leave some pretty terrible families around.