Hi -
I had a look at the image you attached, and understand what you need.
I am a Microsoft Access developer and have worked extensively with date and time type applications, as is required in your project. Access has fantastic reporting abilities for what you require, for example summarizing work and rest hours per week, per month, per staff member, basically any time of reporting that you require.
Supporting that, and ensuring that the data is captured properly, Access offers user-friendly input screens that can be passworded to ensure that information is protected from being over-written, and depending on the user level that is required.
Please get in touch if you have any questions for me or would like your application to be written in Microsoft Access.
Regards -
Carolina