We are a small staffing firm and we recently placed an employee at a company that requires her to work 50-60 hours per week. She has a title of Director and manages many people but she is an hourly employee. Under California law, is she entitled to overtime/doubletime?

Probably. The problem is this. If you want to claim that the employee is Exempt, then you (the employer) is required to actually follow the rules associated with the specific exemption claimed (and there are a lot of possible overtime exemptions).

Based on what you have said, you are probably talking about the Executive exception. There are a number of rules associated with this exemption, and you are not following the one that says the employee must be paid a salary of at least $640/week. Your decision. But when you decided to not follow the rules, then you legally also decided that this employee is not Exempt. Not legally anyhow. While I am quoting the stricter CA rules, there is also a federal rule requiring a salary of at least $455/week for the Executive exception.

CA rules

http://www.dir.ca.gov/dlse/FAQ_OvertimeExemptions.htm

executive exemption
A person employed in an executive capacity means any employee:

Whose duties and responsibilities involve the management of the enterprise in which he or she is employed or of a customarily recognized department or subdivision thereof; and
Who customarily and regularly directs the work of two or more other employees therein; and
Who has the authority to hire or fire other employees or whose suggestions and recommendations as to the hiring or firing and as to the advancement and promotion or any other change of status of other employees will be given particular weight; and
Who customarily and regularly exercises discretion and independent judgment; and
Who is primarily engaged in duties, which meet the test of the exemption.
An executive employee must also earn a monthly salary equivalent to no less than two times the state minimum wage for full-time employment. Full-time employment means 40 hours per week as defined in Labor Code Section 515(c).


Federal rules

http://www.dol.gov/esa/whd/regs/compliance/fairpay/main.htm

However, Section 13(a)(1) of the FLSA provides an exemption from both minimum wage and overtime pay for employees employed as bona fide executive, administrative, professional and outside sales employees. Section 13(a)(1) and Section 13(a)(17) also exempt certain computer employees. To qualify for exemption, employees generally must meet certain tests regarding their job duties and be paid on a salary basis at not less than $455 per week. Job titles do not determine exempt status. In order for an exemption to apply, an employee’s specific job duties and salary must meet all the requirements of the Department’s regulations.

I want to make sure I understand this statement:

"executive exemption
A person employed in an executive capacity means any employee:

Whose duties and responsibilities involve the management of the enterprise in which he or she is employed or of a customarily recognized department or subdivision thereof; and
Who customarily and regularly directs the work of two or more other employees therein; and
Who has the authority to hire or fire other employees or whose suggestions and recommendations as to the hiring or firing and as to the advancement and promotion or any other change of status of other employees will be given particular weight; and
Who customarily and regularly exercises discretion and independent judgment; and
Who is primarily engaged in duties, which meet the test of the exemption.
An executive employee must also earn a monthly salary equivalent to no less than two times the state minimum wage for full-time employment. Full-time employment means 40 hours per week as defined in Labor Code Section 515(c).

So if these items falls under my or the managers below me, then we are all not authorized for any overtime worked over 40 hours, is that what I'm reading here?

I am not sure what you mean by "authorized". You seem to be using that word in way that CA and the feds do not. Maybe you are talking about whether payment is due for time worked, or maybe you are talking about the employee being able to set their own hours or maybe you are talking about something else.

An Exempt Salaried employee (assuming that is what you are) has no legal right to paid overtime. A Non-Exempt Salaried employee must be paid overtime for any hours worked past 40 in the workweek. The key is however for either type of employee the employer gets to determine what hours worked must be worked. Legally the employee has no say what-so-ever in what hours must be worked.