Well, through could mean:
"up to and including (a particular point in an ordered sequence)."
"moving in one side and out of the other side of (an opening, channel, or location)."
The trend continued [through] to April.
If the above sentence was "The trend continued through April," I could tell you with confidence that this means that the trend continued throughout/during April.
As it stands in the original sentence, I'd say more context is needed. Perhaps it wasn't expected for the trend to continue until April, and therefore it continued "through" despite our expectation? it's really hard to tell without additional context.
The trend continued to April.
Although not necessarily incorrect, this is not a a common phrasing style. You would use to with months mainly when you want to define start and endpoints:
I worked as a programmer from March to April. (here still, until is better to avoid ambiguity)
The trend continued until April.
The trend stopped when the month of April started.