I figured it out, you can do it via plink as follows:
p-link --bfile datafile1 --keep LIST1.txt --make-bed --out
Where LIST1.txt is a list of family ID's and individuals. So say if you wanted to extract Family 1, LIST1.txt would consist of:
Family 1 TS11339
Family 1 TS11233
More information can be found at the plink website.