Seems to me there should be a better way then what you have described, though I do not know what it would be.
Seems like from this point it should be straight forward. Run a SELECT query on the new table to retrieve the results, then use an INSERT query to add it to your target table.
$results = mysql_query("SELECT * FROM new_table");
while($row = mysql_fetch_array($results)){
$resluts2 = mysql_query("INSERT INTO target_table VALUES(0,$row['val1'],$row['val2'])",$mysql_access);
}
$results = mysql_query("DELETE FROM new_table",$mysql_access);
This is really simplified, but basically that would do it. Though I would check that DELETE query, I don't remember if that is the exact syntax, but it should delete all rows in the new_table so you start fresh next time you use it.