Hi Barbara! Yes, your info is correct. It is a Japanese Barberry; it is mildly toxic to people & animals (that's why the deer & rabbits don't eat it!). It's considered an invasive plant though it hasn't been banned from sale in Ohio...yet. Birds come along & eat the berries; then they fly away & poop out the seed part of the berry; then another plant grows somewhere. The barberry is an aggressive grower so it will crowd out native plants.

This plant is often a home for the black legged tick (Deer tick) which carries Lyme Disease. I don't know if you have pets, but keep them away from this plant just for the fact there might be a tick hiding in there!

Now for the removal part of your question:

manual removal is difficult. You've noticed the thorns?? Also the roots are small & thin. When you break off a plant from the root, another plant will grow from the leftover root(s). You can spray the leaves with a 2:1 mixture of glyphosate & triclopyr. You can spray the leaves at any time. It may take several rounds of spraying.  The most effective way is called "stem treatment." You want to cut the plant as close to the ground as possible. If you use the oil-based triclopry, you can spray the leftover stems at any time. If you use the glyphosate (water based) you MUST spray when you cut (pruners in one hand, the spray bottle in the other; cut, spray, cut, spray, cut, spray, etc).

The listed chemicals are considered non-selective meaning they will kill any plant they touch - be careful where you spray. It is important that you wear protective personal equipment (gloves, long sleeves & pants, eye protection, & that mask we all have now). The label on the chemical bottle is the LAW - you must follow all instructions on the label. Also, remember those thorns?? Wear protective equipment to protect your skin from being punctured especially when you're going to spray chemicals.

Enjoy your garden!!