Swamp White Oak Trees
Our back yard has four mature Hawthorns that are infected with woolly aphids that might or might not be treated with a systemic pesticide. If we plant a Swamp White oak tree in the back yard, will the aphids adhere themselves to these types of trees? Do we need to treat the Hawthorns before planting or plant the new tree in the front yard?
Denver County Colorado aphids
Wooly aphids tend to occur on apples and crabapples, while Hawthorn mealybug, an insect pest covered in white wax, occurs on Hawthorn. Either one shouldn't prevent you from planting the Swamp White Oak in the backyard if that's where you want it.
As an alternative to systemic pesticides to treat and control your pests, consider using a horticultural oil in the dormant season. It effectively smothers the over-wintering insects/eggs but causes less damage to pollinators.
Here's some additional information: http://extension.colostate.edu/topic-areas/insects/insect-control-horticultural-oils-5-569/