You have things the wrong way round.
Why not stay somewhere that has plenty of facilities for children and then travel to Mabini St for your meeting?
All of the tourist areas of Metro Manila are safe and realistically, no one area is safer than another but avoid poorly lit areas at night.
Manila Hotel is in an excellent choice because it's not far from Robinson's Ermita and SM City by City Hall as well as Children's Museum (Pambata Museo), Luneta Park, Intramuros and Manila Ocean Park.
Although you don't say how long you will be staying, there is sufficient close by to keep children amused for a week or more.