Is my way of dealing with my in-laws—by dedicating two hours a day to them—correct, taking into account my desire not to spend more time with them, and my eagerness to please Allah without infringing upon my own rights? And is it Islamically permissible to request an independent home in the future, near his ailing parents' house?

May you be rewarded with good for your keenness to maintain a good relationship with your husband's family.

You are not religiously obligated to socialize with your husband's family, sit with them, or have lunch with them. If you do so for the sake of maintaining good relations, it is good.

As a wife, you have the right to have an independent home with its own facilities and entrance. If the part of the family house you live in has its own private facilities and entrance, then it is sufficient, and your husband is not obliged to provide anything else.

Patience, deliberation, and wisdom are required in dealing with problems between a wife and her husband's sisters.