If the child's mother is that unstable and unable to offer consistently responsible parenting it may be time to seek a change in the custody arrangement. In the meantime, all you can do is extend yourself for this boy's benefit whenever you can. That's exactly what I would suggest, even if you anticipate his mother may renege at any point. The only way stability will be achieved is through a change is custody.
Thank you for your advice. I will do it with an open mind