Carole Highlands Elementary School is in Prince George's County. You can verify this by simply searching its name in Google.
As to the Carole Highlands *neighborhood*, that's different.
Everything within Takoma Park's city limits is in Montgomery County. The border between Montogomery and PG Counties in that neighborhood is approximately 14th Street: WEST of 14th Street is within Takoma Park city limits and therefore in Montgomery County. EAST of there is in Prince George's County and is not actually within the city limits of Takoma Park.
Highland View Elementary School is EAST of the border and is clearly in Prince George's County. And its web site confirms this.
While the agent is correct that individual school attendance boundaries may change, shools themselves do not change between counties. The only political boundary change in the area happened in 1997 when all of Takoma Park was unified into Montgomery County.