Recently I had a discussion with someone and the following examples were brought up. I was told that I was wrong, but as a native speaker I don't think any of my explanations of the meaning were wrong, regardless of whether they are classified as adverbials. If I am wrong, can you explain why, preferably giving evidence showing that native speakers do not conceive of these adverbials in the way I claim?
A few days every month, she goes to the park while he stays at home.
The adverbial "a few days every month" modifies the whole sentence "she goes to the park while he stays at home", because it is incorrect to split it into two as in "She goes to the park a few days a month, and he stays at home a few days a month." So the adverbial must be modifying the concept as a whole and not the two verb phrases separately. This is in contrast to the adverbial prepositional phrases "to the park" and "at home", both of which modify only the corresponding verb. Specifically I would parse it as follows:
( A few days every month ) { { she { goes ( to the park ) } } while { he { stays (at home ) } } }
Similarly:
Once a year, a new guard takes over.
The adverbial "once a year" does not modify just the verb phrase "takes over", since it is not that the new guard repeatedly takes over every year (from himself!?). Instead, the adverbial modifies the entire sentence "a new guard takes over.", specifying how frequently that event occurs.
Also:
John rowed, and Jill walked, slowly.
I said that it is possible for "slowly" to modify only "walked", and also possible that it modifies both "rowed" and "walked". The reason is that the two commas allow the sentence to be split in two different ways, resulting in the two different interpretations. My interlocutor, however, did not agree that "slowly" could modify just "walked" alone.
And for:
A few days every month, he goes cycling.
I would say that it is likely in the mind of a native speaker that the adverbial "a few days every month" modifies the whole sentence "he goes cycling", but it is also possible for it to modify only the verb phrase "goes cycling". My reason is that in the first two examples above that is clearly the default way the adverbial is mentally processed since it is set off from the rest of the sentence by a comma/pause. In contrast, when we want the adverbial to modify only the verb phrase, we usually put it right next to the verb phrase, unless we want some special effect such as in the third example.