Hi Sonni - Yes, there are several things I would suggest she be tested for. First, since her thyroid test was a little off, she should ask for a full panel - thyroid antibodies plus FREE T3 and FREE T4 as well as TSH. Her weight gain and fatigue are certainly suspicious. She should also request a serum B12 and MMA - measures of B12 deficiency, which can be related to vitiligo. Folate should also be checked. Here's some references on using B12 and folate: http://www.ncbi.nlm.nih.gov/sites/entrez?cmd=Retrieve&db=PubMed&list_uids=1516378&dopt=AbstractPlus
Also, she should be screened for celiac disease (gluten sensitivity) since this can predispose to many other autoimmune conditions. I recommend anti-gliadin IgA and IgG, anti-ttg, and total IgA. (Because many celiac patients are IgA deficient, this can skew the results, so it's important to check the total IgA).
Once you have her results, post them back to me. (And can you post her current thyroid test result now?)
Yes, the predisposition to autoimmune diseases can run in families, even if it takes the form of different autoimmune diseases in different people.