This doesn't add up.
So the op has three children, and the op's mum has made an allegation that the op tried to strangle one of them. The op has a volatile relationship with the son by her own admission... although says there was no violence.
Social services have become involved and have presumably spoken to the child who has corroborated the grandmother's allegation... and now social services have advised the op that the child shouldn't be staying with her for the time being. They are however prepared to let the child come to her house, unsupervised, for tea....? 
And meanwhile the op has two other children who are not even on social services' radar,
why not? If SS were investigating a serious allegation in a family where there were children present they wouldn't just focus on one child and leave the rest to get on with it.
And the op's response to this has been to allow the child to go back to the person who has made the allegation against her - why?
I'm sorry but I don't believe that we are being given the whole story here.
If the mum has made an allegation that is one thing, but the child has backed up what she has said, and he will have been interviewed independently of the mother and still he has backed up the allegation...
At best this is clearly a very disturbed child - one who is prepared to make allegations against his own mother, so there is clearly something not right within this family setup... he at the very least needs some psychological help, and it is unlikely that your mother's attitude is entirely responsible for that.
I understand why you wouldn't want to give all details here possibly for fear of being judged, but tbh it would be better for you to get legal advice.
I also think it is dangerous for people here to be giving the advice to call school/collect the child etc when for all we know the child may well be at risk.