The bugs belong there - leave them be. The briars you CAN pull out, but you may need leather gloves to do it. Or you can cut them down with pruners and spray regrowth with RoundUp. Start at the outside edge of the patch and gradually work your way around the outside until the patch gets smaller and smaller. It took me several weeks of effort to get rid of mine, but I only worked on them an hour or so each weekend day, and not at all during the week. It helps to get started in late winter while the plants are relatively small. It also helps (though it takes longer) to chop each cane into smaller pieces so you don't have to handle long, whipping canes that have a tendency to reach around and grab the back of your head!

Be patient amd don't give up. You can beat these weeds.

You could dig them out. You'd be going two jobs in one: digging out the weeds and digging your garden in preparation for planting/putting down a lawn. You'd also get an idea of the condition of your soil. It's what we did in our garden when we moved in - we dug over every inch of it to remove the brambles and other weeds, and discovered tons of buried rubble, which also needed to be removed.

I have been fighing with briars in my flower bed for years and to say the least they continue to win. If I spray them will it kill my other plants in the bed? I don't want to kill my other plants but they are taking over.

It depends on what you use. Herbicides with glyphosate as the only active ingredient will affect only the plants they are applied to, but you will need to be very careful to keep any spray, drips, or drift off of your desirable plants. Other kinds of herbicides may or may not be root active and may affect non-targets.