The following sentence is extracted from 親の七光り
権力を持つ親を持った子供
Why can't 持つ be used in both?
権力を持つ親を持つ子供
Or 持った?
権力を持った親を持った子供
How about this?
権力を持った親を持つ子供
The following sentence is extracted from 親の七光り
権力を持つ親を持った子供
Why can't 持つ be used in both?
権力を持つ親を持つ子供
Or 持った?
権力を持った親を持った子供
How about this?
権力を持った親を持つ子供
The short answer is that you could use the others, but if you compare, probably 権力を持つ親を持った子供 is the most natural.
The basic points are:
I guess it depends a lot on the nature of the actual words whether た-form or the dictionary form is preferred. For example, 障害を持った子供を持つ親 is equally natural as 障害を持つ子供を持った親. A possible explanation is 権力 is much more volatile than disabilities (and repetitions tend to be avoided).
Also, if there is no clause with 持つ (as in 権力を持つ), Xを持つ子供 is perfectly fine.
Here (to me) …持った子供 is fine, but 持つ is slightly more natural.