Toddler groups do exist although many mums have returned to work by the time their children reach this stage.
For non-Dutch residents there are a reasonable number of associations and informal groups who meet with young children. The local stadhuis will have details. Consulates are another useful source of information on such groups. Sometimes the local municipal websites have information on playgroups and activities for English speakers.
Most Dutch towns and cities are well equipped with parks and recreation areas. Entry is usually free and many have play areas specifically designed for young children to play safely. Parks are a municipal responsibility and are typically well cared for. Find out about local parks from the municipality or Local Tourist Information Points (TIP).
During school holidays in particular special activities aimed at small children often take place in parks or museums. Many are free or very low cost. Again the local TIP will advise.
Public transport throughout Holland is reliable and easy to use. Under fours travel free on all forms of public transport.
Kidsgids is a series of book for parents which outlines things to do and places to go for families with children from newborn to 12 years. An English edition, Kids Guide, is a 320 page book produced specifically for expatriate families moving to and living in the Netherlands to help discover and understand the country and its culture, nature, sports, shopping and restaurants. The book can be bought online.