On checking I can find no direct relationship between the persons you gave and George Mellor. George had about 20 cousins as well as two or three sisters. For the next generation back - Georges father was called William (b. 1764) and his fathers family were John and George and Sarah. Their father was John (b.1740, d.1811). The only possibles for Edmund - assuming he was born in Yorks - on the IGI were born 1781, 1785 and 1786. Their are none listed in the IGI for 1775 to 1780 that are relevant. Of course the IGI is not all inclusive - I shall be getting the relevant Parish Registers (for myself) in about a month so if I get any more info then, then I'll post another follow up.
One other point of interest is that on the same day as Edmund Mellor married Lydia Brook in Almondbury (I think it was), a Joseph Mellor married a Mary Brook in Kirkburton on the same day - coincidence?