did he face any disputes with his family?
Yes, there was a rivalry with his brother-in-law and first cousin Frederick William I of Prussia.
George II of Great Britain
rivalry between George II and his brother-in-law and first cousin Frederick William I of Prussia led to tension along the Prussian–Hanoverian border, which eventually culminated in the mobilization of troops in the border zone and suggestions of a duel between the two kings. 
who was the king of england in 1755 George II. whom was he married to? Caroline of Ansbac.
wiki:11539031
George II of Great Britain [SEP] Family problems
Further friction between them followed when Frederick excluded the king and queen from the birth of his daughter in July 1737 by bundling his wife, who was in labour, into a coach and driving off in the middle of the night. George banished him and his family from the royal court, much as his own father had done to him, except that he allowed Frederick to retain custody of his children.