My family's relationships are complicated by a high number of addopted, half, step and ex- relationships. This sometimes leaves me at a loss when I'm trying to describe how someone is related to me. Alternately, I spend a good minute or two describing the chain of links that make up the relationship.
office mate and I came up with a system that can be used to create a single word that exactly describes any given relationship.
The system consists of a group of sylables. Trace the path from you to the other person in terms of parents, children, siblings and spouses. For each link in the chain, add another sylable.
For example, I have half-brother with my mom as the common parent. This relationship has two links - my mom -> her son.
The sylables for every link in the relationship chain have two letters plus there are some optional modifiers that could be added to make a third letter.
The first letter is a consonant indicating the sex(es) of the people:
p - male
m - female
z - don't know or decline to specify
b - both male and female
The second letter is a vowel indicating the type of relationship:
a - parent
o - child
i - spouse
e - sibling (but only for full natural siblings)
The modifiers are:
s - more than one (bas is both parents, for example)
x - ex- (spouses)
d - addopted
f - foster
n - next/future/later (spouses)
v - evil or wicked (pamiv = wicked step mother)
The special sylable "fam" refers to the group of family members that an indicated person normally is close to. "mifam" is your wife's family.
Examples (from my family or families of people that I know):
mapo (half brother through my mom)
mimemopa (guy that sister in law had a daughter with)
mimespi (brothers in law through wife's sisters)
basbasbosbos (all of my first cousins, including those through half relationships)
mipominmapinso (wife -> son -> fiance -> mom -> next husband -> son = step brother of step-son's fiance)
Researching this idea, I've seen several systems for genealogy that involve *numbering* relationships, but that's not terribly useful in conversation.
In the Robert Heinlein novel "Citizen of the Galaxy", the protagonist spends some time on a large family run trading ship. The ship-board culture has it's own "secret" language that includes an extra set of words for naming relationships. The book doesn't explain the system or give any examples, though.