Sounds like you are worried, and rightly so, sounds like your relative is very aware he is driving when he shouldn't be, he may be breaking the law, he may have already had his license revoked by the DVLA and not telling you.
I get the underlying question in your post is you probably know all ready that he shouldn't be driving and wonder what you should do about it? I think you already know the answer to your own question if you are honest with yourself,
I feel for you you are in an awful position and I wouldn't like to have to make this kind of call about someone I care about, no one can tell you what to do but you have to make a decision you can live with.
What would I do? Try talking to him again and see if I could get through to him how much he is putting himself, his child and other road users in danger,
If he still made all those claims he is making I would tell him that if he didn't face up to what was happening I would inform the DVLA and let them take it from there.
Good luck with whatever you decide to do but I think you realise you need to do something