Creating regular expression with sub sequences of strings
The following regular language should match your specification. I've used a slightly different notation than yours, denoting $(a \cup b)$ as $\{a,b\}$.

$\mathcal{L} = c \cup c \{a,b\} \cup c \{a,b\} \{a,b\} \cup \{a,b\} \cup \{a,b\}\{a,b\} \cup \left( ((\{a,b\}c) \cup c)? (\{a,b\}\{a,b\}c)*\right)$

$?$ denotes repetition  zero or one time, and $*$ repetition zero or more times.

It can be written in a more compact representation as:
$\mathcal{L} = c\{a,b\}\{a,b\} \cup \{a,b\}?c?\{a,b\}? \cup (\{a,b\}?\{a,b\}?c)?(\{a,b\}\{a,b\}c)* $