I have heard of being sent packing. (It's happened to me more than once) But, "packing from the hills" is new to me.
I would regarding "packing" as a participle, modifying "people". But, I suppose that "packing" could be considered to be acting adverbially, answering "how?" The prepositional phrase "from the hills" is clearly adverbial. Now, whether it modifies "packing" or "sent", I guess, must be up to interpretation.
[Not an R-K person] I regard 'send packing' as a multi-word verb, with a meaning similar to 'dismiss, evict, send off'. It would seem to me that 'from the hills' can be analysed in this sentence as if 'sent packing' were a single-word verb.