When Lord Parker sent Lord Bernard to the aid of Lord Kite, he did it with the hope that both sides would use this to familiarize themselves with how the other fought, thus helping them fight better as a single coherent fighting unit in the future.
Plus, Lord Parker was also interested to see if what he had read about the Margraves family troops was true, that they were almost as skilled as any ducal forces, especially when it came to naval fighting
Being a scion of one, such a bold statement inevitably pricked at his ego a bit.
But all such considerations were turned moot when Lord Bernard decided to ignore that objective, leaving Lord Kite to himself and instead setting his eyes on the bridge- the same bridge that was currently being overrun by Alexander.