A "power dynamic" is the way different people or different groups of people interact with each other and where one of these sides is more powerful than the other one. See Wikipedia for a definition of social/political power:
In social science and politics, power is the ability to influence or outright control the behaviour of people.
The use of power need not involve force or the threat of force (coercion). At one extreme, it closely resembles what an English-speaking person might term "influence", although some authors distinguish "influence" as a means by which power is used.
The quote you mentioned was:
...how important it is to theorize the diverse and changing power dynamics between the different genders, races, classes, and ages of household members.
The intention of the quote is to make you as the reader aware of the importance of thinking about power dynamics, meaning that you should think about which group(s) influence(s) which other group(s) in respect to:
- different genders
- different races
- different classes
- different ages of household members
To not stir any discussion, let's look at a simplified version of the last example: different ages of household members. In general children should obey their parents - the power dynamic is that parents have power/influence over their children. That is what you should think about: How is this expressed? Is this right? Is this how we as a society want it to be?
A power dynamic is not necessarily a bad thing, but it can be used that way if you want to show that a certain dynamic is not desirable and want to illustrate what the problems of the dynamic are and how these problems could be solved. Especially your second quote about asymmetric power dynamics illustrates how the author wants to show the reader that one group holds power over the other.