For example: when using inheritance with classes in Java, I have a parent and two classes which inherit from that parent. Do I refer to these as 'children' or as 'childs'? In other words, what is the plural of 'child' in terms of class?
Since you specifically referred to the Java programming language, the official terms are superclasses and subclasses, not parents or children, according to the Java Language Specification, section 8.1.4.
The concept of parent and child belongs to the Unified Modeling Language, which uses genetic relations to model class inheritance. Where the UML specification refers to plural classes with inheritance, it does so with the terms parents and children. See the UML Specification, Section 126.96.36.199 for such an example. Childs would be completely incorrect.
Many people regularise to computer mouses because when referencing something so completely different to the "original" meaning, they feel it's a "different word" (which allows them to ignore the irregular form).
But it's important to note that "child" in the computer context is nowhere near as familiar to ordinary mainstream Anglophones as "mouse", so they'd very rarely be exposed to other people overruling the irregular plural. And in contexts like this, although people might in principle be more than willing to adopt the regular form for the "neologistic" usage, few of them really want to be "early adopters" (sometimes, in case others think they're simply being ignorant).
The other important factor is that whereas there's no easy "workaround" for the problem with mice/mouses, it's not usually a problem to simply refer to child classes rather than children.
The FreeBSD manual page for the ps command (process status) says, among other things:
-S Change the way the process times, namely cputime, systime, and usertime, are calculated by summing all exited children to their parent process.
FreeBSD is based on Berkeley unix, so other unix varieties probably also use the word "children" as the plural of child. However, the term "child process" and thus the plural "child processes" may be preferable in many contexts.