realistartinoz

Hi oldduck.
What a caring person you must be, let alone observant of things that may be not quite right somehow.
If you can't 'reach' the boys mother, what about the young fellas father; your partner? He is still in the position of acting as a responsible parent for his son, even if he only sees him every second weekend. If your partner is aware of any problems and shares your concerns, he certainly can act on those concerns. He is his dad. With your support ('one step behind'), he can seek the advice of, for example, a doctor who could refer him to a paediatrician, psychologist and/or another appropriate health professional to assess if there are any issues of concern and the subsequent assistance your partner's son needs. (ps. our local councils have a community health service who you can speak to and visit. They have health specialists, eg. psychologists, who can assist).
We all, as parents, need to honour the needs of our children and the child themselves has the right to have such needs met. Add that to the kind heart you have and a hopefully responsive partner (whom also recognises areas of concern?), and the young boy will on the road to happier, less frustating experiences in his childhood. This could also be a pivotal point of intervention which he may need and which could benefit him for his future.
Your partner could also contact 'others' who may be involved in the boy's life. For example, the kinder teachers, health nurse etc., who can be asked if they share the same concerns about the lad, according to their observations of his behaviours.
Good on you for being caring and asking such questions. Sometimes it takes an 'outsider' to raise attention to the possibility a child requires assistance of some kind.
Another thing to consider is, if the boy's mother (or father?) is not responsive or receptive to your input (maybe because you are her ex's new partner), they may be unaware of what you've observed with the lad, or they are in some sort of denial that anything is problematic with him (boy).
Maybe the young boy's behaviours are in response to an emotional 'struggle' with, for example, the situation of mum and dad not being together, your new relationship with the father............who knows. It really is not for me to guess any of this, as I don't know you.
But, I wish you all the best and I hope all turns out well for your partner's son.