"BROTHER-in-LAW" is a combination of BROTHER and LAW. That means it is a "compound" sign. You generally get rid of the first part of the sign LAW. Some people even get rid of the last half of the sign brother.
BROTHER: (This is a popular version of the sign "brother.")


LAW:




This is how I recommend you sign "brother-in-law"
Sign brother, then place an L on the palm:



Now, check this out.
BROTHER-IN-LAW:
When you see "in-law" as part of a phrase such as "brother in-law" you
might
see it drastically shortened to include only the first part of the sign for
brother and the last part of the sign for law.




SISTER-IN-LAW:
When you see "in-law" as part of a phrase such as "sister in-law" you might
see it drastically shortened to include only the first part of the sign for
sister (girl) and the last part of the sign for law.





IN-LAW: Here is an "English" way to show "in-law." You just sign
"in" and then sign "law."
But please note that most of the time the sign "in" is dropped when you are
signing compound concepts like "brother in-law." (see above).
I don't know of anyone who would actually sign "IN" plus "LAW"






Animation: Brother in-law (version 1)
Animation: Brother in-law (version 2)