On my farm I try to
fence my animals out of watery locations so as to preserve the watershed and aquifer. That does not mean the water cannot be used for livestock, but rather just keep them from slogging through it.
Obviously I do not know much about your place, but a great way to "develop a spring", is to use cheap drain tile and try and capture the water upstream and channel it down to the lowest point in the weep spot where the old backhoe dug. Fan the drain tile out as much as possible so it gathers from as big a wet area as possible into one collection point. I'll call this a sump. You can buy
concrete tiles 4 feet in diameter purpose made for this, use a plastic 55 gallon drum, or if plastic and concrete is not to your liking; a circle of stones to hold back the soil as you make your own sump. Dig it as deep as you want to go down, put a gravel base in and you
should have clean water pulled from a broad area.
From that sump you can either install a hand pump, a
solar pump, or if close enough to electricity, a electric pump and pump the collected water to stocktank to water livestock. This will keep the area from being contaminated by livestock manure, and keep it from going downstream to your neighbors.