what is the name of the office in chapala, but I think part of the state government ....

The Registro Publico?
I don't think wills are there, though.

The Registro Publico is where deed information is, and now that I think about it, you may be right that that is where wills are too. I would imagine that it is the registry of all the public legal documents in the municipality.

I can tell you what I did several years ago when I wanted a copy of the escritura and history of ownership of a piece of land my family owns:
I first got a historial catastral from the same place you get your property tax info in the municipal building in Chapala. (The counter at the back left)
This gives you a description of the land and a list of all the previous owners with each owner's escritura publico numero.
With those numbers I then requested copies of the escrituras at an office that is at the same site as the Recaudadora on Degollado. The office is off the courtyard on the right. With the escritura number they looked up the folio number (ledger or file number), I submitted the request, paid, and went back several days later for the copies.
That office has computers people can use (I didn't). You may be able to skip the historia catastral step if you're researching property, and the computers may give access to other types of documents (like court filings, etc).