The prayer in a work setting issue is a bit like breast feeding in public (but not quite). Both are normal healthy human activities. Both ideally are conducted in a setting in which everyone involved helps facilitates the process and no one feels victimized. Both have "the right" to be conducted in public (well, I wish this world would get a little bit more tolerant of nursing mothers and the babies that need their milk. We are mammals after all! We are classified as such because we nurse).
In my own spiritual practices as an agnostic yogi, I prefer to do my full blown out expressions of spirituality in a setting that is conducive. I would be horrified if I went to a staff meeting and the other staff members had to do sun salutations or pranayama against their will. It demeans my own personal practice as a yogi and turns it into a spectacle instead of the special experience it is. However, I have been known from time to time, do a few mudras (hand yoga/ special hand signs) or silently chant to myself before a big test or a dreaded meeting. Actually, during a meeting, I can practice prana (breath control) discretely without anyone being aware.
Its too bad that the OP's coworkers are not more sensitive to other people's spiritual practices and don't make their own spiritual practices more special by not including them in a meeting ( what I mean by that is that a work meeting is a relatively mundane time, not exactly the time to get a marriage proposal or announce the birth of your child, very unromantic, usually under fluorescent lighting and in uncomfortable chairs). A simple moment of silence will suffice. If they insist on a group prayer for whatever reason (my own spirituality is special by itself and does not need numbers, but I will say that a roomful of people breathing in unison is cool, but not something I need at work).
Nursing moms should absolutely have the freedom to nourish their infants anywhere and anyway they please, just as any one of any faith should have the same freedom for themselves, but with that freedom comes responsibility and the need for tolerance. I wish I could nurse and if I could, I would probably only want to nurse in a zen like space so it would be a fantastic baby mommy mind melding experience, but I understand that infants have needs that are unscheduled and sometimes people feel the need to talk to God/Godess/Vishnu/ Yesu at the last minute. (Actually, the semantics of many of our phrases for last minute/ unprepared have a prayer element in them, if you think about it)
Should nursing moms be confined to unsanitary and uncomfortable bathrooms and back alleys to perform nature's miracle--absolutely not. Should a nursing mom who is at home but has a few close friends over have to hide her baby's needs--certainly not, she should stay put in her comfy chair. I would hope though that she thinks ahead and assesses each situation but I wouldn't mind if it just so happens that she has to do it while I'm around. A nursing mom should use her time with her infant not to make a political/ social statement, but to nourish physically, mentally, emotionally and spiritually both herself and her infant. If life happens and it happens to be in the middle of a parking lot, we'll just have to deal with it, but most nursing moms would rather be elsewhere when the need arises.
Should prayer groups be hidden or confined, absolutely not, but they should position themselves in a way that demonstrates that they think ahead and assess each situation. If it is absolutely necessary, then go ahead, but if it is not, then I would hope that they would respect their god by not creating any casualties or collateral damage through their practices. Again, if they absolutely have to pray in a group with non participants in a room and it cant wait until a more appropriate time, then let it be a moment of silence, reflection, coffee break, bathroom break or something.
Just as I have a last minute need to meditate (which I can do discretely, but I'm not ashamed to do publicly and if anyone asks I use the opportunity not to evangelize but to educate--I was discovered by a classmate doing a handstand before a test in a far off area of my school and I explained that the asana (sanskrit for pose) helps improve circulation to the brain.
If I worked for an organization that 99 out of 100 people where yogis and we made a point of engaging in activities that made that one person feel alienated, I would feel so bad and personally not engage in my practices while that person was around just to support them. It would defeat the whole purpose of my spirituality if I made that person feel bad and alienated them.
If I was one of 99 nursing moms sand we had a staff meeting and 99 out of 100 of us mothers nursed our babies during the staff meeting while one mother felt bad because she either did not have any babies to nurse or could not nurse, I would feel bad for her and out of respect for her take my nursing activities outside of the meeting because I would not want to make a coworker I cared about feel bad in anyway.