We currently have almost 2 acres, but lease 1/2 an acre on a property adjacent to ours to fulfill the 2 acre unlimited animal ag zoning requirement. We raise dairy goats. They sold the property. If we lease a 1/2 acre from another neighbor whose property is not adjacent to ours and we keep a few animals on their property would that fulfill the 2 acre requirement? That is we would have over 2 acres available for our animals to be on, it just would not be directly next to ours, but within 1000 feet.
It depends on the zoning ordinance and the interpretation of the zoning officer or ZBA, but typically minimum lot size requirements for a use zone must be met by fee (full) ownership of the land and the lots must be contiguous (touching) and perhaps even un-subdivided (recombined) into one lot. Most of the time leases don't cut it because the ownership of the land can change, unless you do something other fancy like get an easement for perpetual agricultural use on the additional land that "runs with the land" and binds future purchasers (so they can't buy it, build a house on it, and then complain about your cattle ranching and manure piles.
You may be able to get relief from the minimum lot size requirement from a variance from the ZBA.
If you're talking about ag districts in a non-zoning context, maybe the situation you've described works here, but typically not in a zoning situation.
As always, this is a very general answer about zoning, CA or local ordinances may be different and allow what you're seeking to do as a "use as of right" without further approvals, but if I had to guess, I'd say "no, what you want to do is a problem".
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Land Use / Zoning Attorney
This question is probably too specific to your area to get an answer here, so you should consider consulting with a local Healdsburg attorney. That attorney can review your local code, and see if your specific situation meets those code requirements. In my experience as a Washington state attorney, I would say it is unlikely that by having non-adjacent land you are fulfilling a specific acreage requirement.
Land Use / Zoning Attorney
You don't specify if you are in the County or the City. If in the County, the Sonoma ordinances would apply; if in the City, the City Municipal Code would apply. Either way, it is unlikely that leasing land offsite would qualify under any situation. If you'd like a consultation, I am in Marin County but work in Sonoma as well.
This response is not to be construed as establishing an attorney-client relationship, and provides general information on the subject at hand only.