First of all, I assume you and your wife aren't union. The presumption in California (as in most states) is that unless a contract says otherwise, employment is "at-will," meaning the employer may terminate you, or change the terms of employment, for any reason, or no reason at all, as long as the reason does not violate some provision of law (such as illegal race/sex discrimination, for example). To my knowledge it is not illegal for the company to impose a "no spouses at the same location"...
Subpoenas are orders by a court officer for the appearance of a witness at a legal proceeding. They are subject to limitations for travel distance, advance notice, etc., but most importantly for your case, if I understand it correctly, they must be served on the witness personally or by some other approved method such as certified mail, return receipt requested and returned. Accordingly, if by "my daughter signed for a subpeona that was for me" you mean to say that your daughter signed...