I would imagine that if this child has been sent to boarding school there are already some significant issues in the mix here perhaps wrt his behaviour or relationship (or lack thereof) with his mum.
While on the surface the idea of adopting a child and then potentially unaddopting it when the going gets tough seems shocking and selfish beyond words, in reality adoption is often not the utopian road to parenthood which is perceived by those who have never adopted.
The reality is that adoption breakdowns are incredibly common, and although children who are adopted cannot be unadopted, many do return to the care system for various reasons, often relating to the past which brought them to the adoption system in the first place.
I know of a couple who sent a child to boarding school after they had adopted him because his behaviour was so difficult that he put his siblings at risk. The alternative would have been to return him to the care system, but this way he went to boarding school, and the structure gave him greater stability in his home life, and prevented him from becoming a failed adoption statistic.
I imagine that the "going to his dad's and then not wanting to come home," is just the last in a long line of issues this mum has dealt with with him, and perhaps rather than feeling rejected she feels that she is no longer equipped to deal with the issues he has. Remember we know nothing about this child, the relationship with his parents, or the circumstances which meant he was placed for adoption in the first place.