What could be causing water pressure drop with sprinklers?
Water pressure drops come from two sources:

1) A constriction in the line upstream, limiting the maximum inflow you can get.

2) More demand on the line, producing more outflow than the inflow can fully pressurize.

If a sprinkler zone is larger (serves too many heads), or if more zones are active at once, it will demand more water. Dividing the zone could be one solution. 

If a sprinkler zone's pipe is kinked or otherwise obstructed, it may not be able to deliver as much water as is needed to fully pressurize the line. 

If running the sprinklers reduces pressure at the sink, the point limiting that is going to be upstream of both, and you're probably also seeing pressure drops at the sink when you flush a toilet or run a bath. You can check for restrictions working back toward the source (valves not fully open, for example), but if the shared flow limit is what's coming into the foundation...