Answer: If the little oaks pull right out, they're the result of seeds germinating in the soil. If you need to cut them to remove them, they're the result of underground roots sending out suckers. It's never a good idea to use herbicides to kill suckers because any chemical you use will travel to the parent tree and kill the roots.
Planting near trees is always a risk because the tree roots will naturally gravitate toward moist, nutrient rich soil. Since the roots are supporting large plants, the annuals and perennials in the bed will suffer from the competition. To eliminate tree roots and suckers in your garden beds, you may have to line the beds with a tough barrier such as hardware cloth, or something similar that will be difficult for the tree roots to penetrate yet allows water to drain through it.
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