The sum of $V=U+W$ of a vectorspace V and subspaces $U$, and $V$ I know what the sum of two subspaces is and how we notate but is it ok to write a minus to denote what I hope should be obvious is meant.
So we have $V=U+W+Y$ where $V$ is a v.space and $U,W,Y$ subspaces- ok to write $Y= V-W-U$ ? and define RHS to be $\{y : y=v-w-u $  for some $v \in V, w \in W, u \in U\}$

No, that makes no sense, I'm afraid.
The set
$$
U-W=\{u-w:u\in U,w\in W\}
$$
is exactly the same as $U+W$, because whenever $w\in W$, also $-w\in W$.
There's no way, in general, to recover $W$ from $V=U+W$ and $U$. Just to make an example, let $V=\mathbb{R}^2$ and $U$ be the subspace spanned by $e_1=(1,0)$. Then
$$
V=U+W
$$
for $W$ the subspace spanned by any vector of the form $(1,a)$, as soon as $a\ne0$. Such subspaces are all distinct.
