First off, everybody is under the direct and current supervision of a doctor.
I’m trying to find information on pregnancy and Reiter’s syndrom, but it is a rare enough disorder that google fails completely. There must at some point have been women with Reiter’s syndrome that have been pregnant.
Try different search terminology 
Use “reactive arthritis” intead of Reiter and your searches will get better.
Here are some links that seemed helpful:
http://www.arc.org.uk/arthinfo/patpubs/6060/6060.asp
http://www.orthop.washington.edu/uw/tabID__3376/print__full/ItemID__97/mid__0/Articles/Default.aspx
Your best bet is to start with a general education around reactive arthritis (the eponymic use of “Reiter” is out of favor b/c of his Nazi associations). Here is a reasonable overview: http://www.aafp.org/afp/990800ap/499.html This will help you know if your search terms are leading you in the right direction.
Next, you might try a literature search using the National Library of Medicine as a starting point: http://www.nlm.nih.gov/
Since reactive arthritis has such protean manifestations and a variety of underlying etiologic triggers, it may be hard to narrow down your exact area of interest. In general I assume what you are looking for is an article which reflects a study done of pregnant women who have a diagnosis of reactive arthritis (use “Reiter’s” as a search term as well since older literature may not use the term “reactive arthritis”).
One can think of reactive arthritis as a way the body reacts rather than a specific disease, although in general, the commonest summary would be an individual who usually has an HLB27 antigen and has had a constellation of signs and symptoms (large joint arthritis; uveitis; urethritis) resulting from an autoimmune response to (presumed) antigenic stimuli such as exposure to an assortment of bacterial pathogens (chlamydia; campylobacter; yersinia, etc etc). Bunch of medical mumbo jumbo, I know, but you can see the many trees down which a simple google search will take you.
Some autoimmune disorders may even stabilize during pregnancy, and except for the inheritence of the underlying predisposition (the baby’s chance of also being HLAB27 positive if mom is positive, for example), it is often not an issue. On the other hand, if the trigger was chlamydia, say, well that’s it’s own problem in pregnancy, separate from the reactive arthritis issue. And in general autoimmune arthritides have a very wide range of expression, from minimal to horrible, so in general, generalizations are useless.
I might suggest asking the OB or the rheumatolgist involved for a good review article if your online search proves ineffective. I apologize for not being more helpful myself, but perhaps others here will come to your rescue and zero in on the exact article for which you might be looking. It may help to narrow the focus to one of three questions. Are you wondering about the effect on Mom, the effect on the baby, or the potential treatment complications and/or limitations because of the pregnancy? Regardless, a definitive answer is unlikely from any given source since autoimmune illnesses are so varied in their prognosis and treatments.
Best
ETA: One final trick I’ve used in my medical practice is to take a standard textbook on Obstetrics, say (try the local library or your own OB, e.g.) and find the paragraph (it won’t be much) on Reiter’s/Reactive Arthritis. Go to the cites at the end of the chapter and look for a review article on the topic. Primitive but effective, since someone else has already done the legwork.