Looking for 80s young adult book

[njm]

Hi,

 

I can half-remember being given a rather odd young adult novel by my English teacher, quite a few years ago now (around '86ish!). A lot of the details I can't remember, but I wonder if someone here could help.

 

The plot was, teenage male protagonist is on the run with his sister and a baby(?). They were on the run from their mother, and end up hiding away on an island. I seem to recall the main character having schizophrenia or some other illness which formed a big part of the later plot, and there was also some sort of incest sub-plot(?)

 

A bit vague I know, not least due to the 25-odd year gap, and I'm possibly imagining some of the plot points above - I just remember wondering why my teacher decided to give me such a strange book.

 

Thanks