Water – ny reason to seal/waterproof underground spliced sprinkler cable

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...

You would not use the existing good sprinkler wires to bring the 120VAC out to the valve box. The wires are not rated and approved for that type of use. Place the converter transformer indoors to step the 120VAC down to the 24VAC. The "good" wires could then be used to route the 24VAC outdoors.

I would not use the sprinkler timer in the valve box. It would be very inconvenient to use it in that manner and the underground environment is highly likely to not be friendly to the control unit circuitry. Instead you should install an outdoor timer unit on an exterior wall above the valve box. (Use "outdoor sprinkler timer" in Google to see a selection of possible timers). The better outdoor timers have a lid that closes over the controls to protect the interior from the elements. You could then use a PVC conduit to route the necessary wires from the timer down into the valve box to keep things neat.

Do select the timer as one that works off the low voltage.