There seems to be some confusion around Kevin's time from 12-4 PM M, W, F with his sons, and why it is happening at Britney's residence. Here's what the document says:
In consideration of the Respondent's (Kevin) agreement to Petitioner's (Britney) request that he visit with the children at the Petitioner's home, Petitioner shall use her best efforts to ensure that no third party visiting the house interferes with Respondent's custodial time with the children. Respondent has requested that Petitioner specifically agree that the persons to be at the home during Respondent's custodial times shall be limited to Petitioner, the children's nanny, Petitioner's assistant and other regular household staff. No agreement has been reached by the parties in this regard.
So basically Kevin has agreed to Britney's request that for January he will spend time with the kids at Britney's home and because of that Kevin wants to make sure there's not going to be a lot of people around during those times. I've heard speculation that Kevin needs to supervised - this is not the case.