Solution $A$ :-
Case $1$ : Both parents are together
#ways $= 7 * 6^3$
Case $2$ : No parents together
#ways $= 7 * 6 * 5^3$
Final answer $= 7 * 6^3 + 7*6*5^3 = 6762$
Solution $B$ :-
Case $1$ : All children together
#ways $= 7* 6^2$
Case $2$ : Two children together
#ways $= {3 \choose 2} * 7 * 6 * 5^2$
Case $3$ : No children together
#ways $= 7*6*5*4^2$
Final answer $= 7*6^2 + {3 \choose 2} * 7 * 6 * 5^2 + 7*6*5*4^2 = 6762$