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The style of case with gold plated highlights on a coin silver case was popular in Europe, early in the 20th century. The type of decorative plating is called “galonne”. The case material (coin silver) is 80% silver, and 20% base metal as indicated by the stamp .800 inside the case back. This material is quite soft and prone to denting and wear. The case back has been patched with lead solder in several areas. The dial (face) is vitreous enamel, and appears to be in good condition. The hands are of two different styles, one probably having been replaced. The movement (mechanism) is likely an Omega 19 ligne model as pictured. As to actual history, being a family watch, your family would know more about that than anyone else.
Thank you very much for the insight.
My mother in law's father is in his nineties and still quite lucid, so I'll suggest that she ask him about the watches history while she still can.
She's a fan of Antiques Roadshow (and has been on the Swedish version herself), so the idea of provenance should be familiar to her.