两个逗号之间的with引导的伴随状语是插入语吗 例句附加在下面

两个逗号之间的with引导的伴随状语是插入语吗
例句附加在下面Hunting consists of pursuing a fox across the cuntryside,with a group of specially trained dogs,followed by men and women riding across.

with这里不是伴随状语，而是方式状语，修饰动名词pursuing, 即 pursuing a fox with a group of dogs

你都说了是伴随状语，为什么还问是不是插入语？ 再看看别人怎么说的。