I suspect your plum tree has scales.* They are an insect pest. The sap you see is actually their waste that is called honeydew.* Ants and bees harvest the sweet honeydew and will defend the scales from predators.* Eventually the honeydew grows a black mold called sooty mold.* Is this what you see?
If so, you can use either a horticultural oil or insecticidal soap.* Both would be safe aruond children. I would suggest an horticultural oil called Organocide made from sesame seeds.* Most horticultural oils are made from petroleum.* The best time to spray the oil is in May.* In the meantime you can make your own insecticidal soap.* Be sure to use soap and not detergent as that can harm the leaves.* Spray every 5 to 7 days until they die off and spray early in the day before bees or other beneficial insects become active.
You can see more pics of these pests here, the site I got the picture from.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.