Solving a variant of the Exact cover problem I am trying to solve a variant of the Exact cover problem where every element has to be covered exactly twice instead of once ( i.e. has to be in exactly two sets that are part of the cover).

Now, it is clear to me that this is an NP-complete problem, but I wish to know if there is any hope for some pseudo-polynomial time algorithm to solve this problem.

If relevant, the context arose from trying to recreate polyhedra from their edges: given a set of edges, decide if they constitute some polyhedron, and if they do, give a set of its faces. Thus the set I wish to cover is the set of edges, and the collection of subsets I have is that of objects that can possibly be faces (each containing the edges of the corresponding "face")
There's no pseudopolynomial algorithm for exact cover (unless P=NP), so it is easy to show that this implies there is no pseudopolynomial algorithm for twice-exact-cover, either.

For instance, here's an easy reduction.  Given an instance $(S,X)$ of exact cover (where $S$ is a collection of subsets of $X$), let $X' = X \cup \{a\}$ where $a \notin X$ is a new symbol, and $S' = S \cup \{X', \{a\}\}$.  Now there is a twice-exact-cover for $(S',X')$ iff there is an exact cover for $(S,X)$.  So, if you could solve twice-exact-cover in pseudopolynomial time, you could solve exact cover in pseudopolynomial time, too.