How can a girl reconcile the obedience of her strict parents with her desire for personal independence and avoiding disobedience to Allah, especially when she feels a lack of appreciation and an inability to come to an understanding with them?

Obeying one's parents in what is good is obligatory if it benefits them and does not harm you. You must revere them and be keen to address them with politeness and gentleness. Allah the Almighty said: "So do not say to them, 'uff,' and do not repel them but speak to them a noble word. And lower to them the wing of humility out of mercy and say, 'My Lord, have mercy upon them as they nurtured me when I was small.'" You must strive against yourself and not surrender to whims and laziness, for good morals are acquired through habituation and practice. Increase in the remembrance of Allah and supplicate to Him frequently.