From your description, this looks like Japanese flowering quince, Chaenomeles japanica. For several weeks in the spring, this plant can be a showstopper when it's in blook. Some gardeners grow this plant for its fruits, which is sometimes used to make jams and jellies. However, as you well note above, the plant has wicked thorns and can spread.

You may want to consider using "brush killer" herbicides (or weed killer).  Be very careful to make sure you closely read and follow the label of the product selected. Do not select a product that will move through the soil and be taken up by the roots from nearby desirable plants. Also be sure to note how long the produce persists in the soil as this would affect how soon you're able to replant an area if so desired. 

Before applying the pesticide, cut the branches off at the base of the shrub leaving 8-12"  from the ground. You can do this with a pair of pruning shears. Start at the top of the plant and work your way to the bottom. If the stems are too thick for pruning shears, use loppers or a pruning saw. Be sure to wear thick gloves and protective clothing to prevent injury from the thorns. Apply the brush killer to the cut branches according to the label. A repeat application may be necessary.

Good luck.