There are no planned works on the Central Line this weekend:
https://tfl.gov.uk/forms/12392.aspx
Also, it is the Circle Line that is closed on Sat & Sun, not the Hammersmith & City.
https://tfl.gov.uk/tube-dlr-overground/status/?startDate=2016-04-16T00%3a00%3a00&endDate=2016-04-17T23%3a59%3a59&dateTypeSelect=This%20weekend#line-lul-hammersmith-city
Prove me otherwise. Don't have kids.