From a strict grammatical point of view, there should also be a "with" in the second prepositional phrase of that sentence, so it will read as follows: "Tom gave up the brush with reluctance in his face, but with alacrity in his heart." This makes both prepositional phrases perfectly parallel and balanced in construction.
In practice, though, some writers tend to omit that second "with" on the assumption that its presence would be understood anyway--an omission that may be considered as some form of ellipsis. To me this isn't a very agreeable practice, but I think it is tolerable except in highly formal writing.
