Doesn't solder usually contain lead and/or other metals?  If the metals
become airborne, it is possible that the mom may inhale and absorb some.
When I had looked into lead and breastmilk years ago, there was very little
data on transport to milk from various routes of maternal exposure.  I'd
recommend first getting the MSDSs on what the solder and flux contain, and
then try to search the literature on transport of the chemicals to
breastmilk.   If there are data for the facility on levels of these
chemicals (for OSHA compliance, for example), this may help in assessing
the risks.  Judy Schreiber.