Working day issue

Here you have deployed from parental company to other company. Hence your parental company has to take care of you, but not the deployed company. Hence you should have to work under the instructions of your parental company. If your parental company allows you  for 2nd and 4th Saturday of every month, as rest day, the same should be applicable in your deployed company too. Or otherwise, if your deployed company is utilizing your services, even on 2nd & 4th Saturdays, your deployed company should have to compensate the salary for the two days. Or otherwise, made a complaint to your parental company about this issue.