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I would not transplant them now until fall when weather is cool. Transplanting in the heat of summer causes unnecessary stress to plants. When you do dig them up, you can remove the soil from the roots and see if it is possible to divide the plants safely. These articles may help
https://www.gardeningknowhow.com/ornamental/trees/caragana-pea-tree/pea-tree-information.htm
https://www.gardeningknowhow.com/garden-how-to/propagation/propgen/dividing-plants.htm

It's a shame to lose a mature tree for the sake of a driveway, but yes, tree roots and pavers are not a good match. Beside root length, they expand in girth and can lift and displace the pavers.

If you value the tree, consider alternative routing of the driveway, or root pruning and installation of a root barrier.

According to the Black Walnut Society, this shrub will not be able to grow anywhere near a Walnut. This link will offer more information: https://blackwalnutdispatch.com/the-black-walnut-society/

This article will help you to grow this shrub (You may want to consider a container): https://www.gardeningknowhow.com/ornamental/trees/caragana-pea-tree/pea-tree-information.htm