RE: 12 day itinerary

Hi there! I am planning a trip with my family (5 seniors, 2 adults, and 2 children under 6)
We currently are planning below
5/11 - Arrive into Narita late-afternoon
5/11-5/16 - Staying around Ryogoku Station
5/16-5/20- Staying near Shin-Osaka Station
5/20-5/22- Staying in Yokohama before flying back via Narita

I feel the 14 day pass may not be worth our trip plan.. But I came across a JR 3-Day pass but confused on what it covers.
Should I get a 3-day pass plus the 7-day JR ? Do these activate based on first day I use or does it have to be informed beforehand? Thank you in advance!