Ask Mr. Smarty Plants

Liquidambar styraciflua (Sweetgum) is native to Illinois but we are doubtful whether you can get anything else to grow beneath it. From our webpage on this plant (follow the plant link to read the whole page):

"Conditions Comments: Sweet gum can become aggressive in moist, sandy soils. It is not drought-tolerant and does not do well is polluted areas or small areas which limit root development. It grows rapidly and is long-lived, adapting to a variety of sites. It is susceptible to iron chlorosis in soil which is too basic. Plant only in spring as roots take 3-4 months to recover from the shock of transplanting. Fruits do not readily decompose and and can jam reel mowers."

This member of the Smarty Plants Team has actually had a sweetgum in her yard, in North Central Texas. They grow natively in the more acidic soils of East Texas, and we had seen them there and wanted one for the Fall color. Of course, that was lovely but the little gnarly seed balls that never decomposed and were scary to step on were not attractive features. As the tree grew older, the roots were pushing up our sidewalk and driveway and trying to get under the foundation. That was probably because there was no Mr. Smarty Plants in those days so we didn't know about the invasive surface roots. We eventually had to have the tree taken down, the roots ground out and  the sidewalk and driveway completely replaced; we continued to find those spikey balls in our garden for years afterward. If your trees were planted in 1942, obviously they were planted somewhere that the roots could not cause trouble; for which you should be congratulated.

Now, about planting Hydrangea quercifolia (Oakleaf hydrangea) beneath those trees. Here are the hydrangeas' Growing Conditions, from our webpage on it:

Growing Conditions

"Water Use: Medium
Light Requirement: Shade
Soil Moisture: Moist
Soil pH: Circumneutral (pH 6.8-7.2)
CaCO3 Tolerance: Medium
Soil Description: Moist, fertile, well-drained soils.
Conditions Comments: Susceptible to sunscald, chlorosis in alkaline soils, and winter dieback. Many weak, brittle canes are easily broken in wind and ice. Forms colonies from a shallow root system. Canes can be cut to the ground every two or three years to keep the shrub smaller, but if the canes are allowed to grow, the naturally peeling bark is attractive. Pest free. Prune immediately after flowering."

As you can see from this USDA Plant Profile Map, this plant does not grow natively in Illinois at all, the closest native state to you is Tennessee, and throughout the Southeast. We always check on that because if the plant does not normally grow in a region, it could very well be because the soil is wrong (hydrangeas also need acidic soil), it is out of the USDA Plant Hardiness Zone or the growing season is too short. Here is another article on the oakleaf hydrangea.

Bottom Line: There is nothing to stop you from planting these hydrangeas, one of the only two native to North America; however, consider you are dealing with a plant not native to your area, you are going to have to severely disturb the roots of your treasured tree, and the hydrangeas still might not survive. Not only that, but the sweetgum, which belongs where you have it, obviously, could be so damaged that it might die. We hate to be so negative, but we feel you are entitled to know that you could spend a lot of resources (time, money, water, back muscles) and end up with neither trees nor bush, or at least a damaged tree.

Perhaps now you understand why nothing else has wanted to grow there. While many plants, including the hydrangea, will tolerate that much shade, few will tolerate that much competition for space and water, with the tree. Because of the age and beauty of the sweetgum, we would definitely vote for preserving that. You might consider putting about 2 inches of a good quality shredded bark mulch on the root area of the tree. This would protect the roots from excess heat or cold, and since you would no longer mow it, those surface roots would not get in the way of your mower. The mulch would have to be replaced periodically, but as it decomposes, it will go down into the soil beneath the trees, assisting in good drainage and making it possible for the tiny rootlets to easily access nutrients and water from the soil.