The v variables in the KR file always refer to the mother. Apart from the height and weight measurements that are obtained during the household interview, all the information about the children in the KR file comes from the woman's interview. The mother is the respondent and she is reporting on her biological child.
If you want, say, the distribution of v106 (level of education) for all women, you should get that from the IR file, which has one case per woman. If you calculate the distribution of v106 in the KR file, it will refer to the mothers of children born in the past five years, and will repeat the mothers who had more than one child. I would say that it SHOULD do that, because the units are children and you are using the education of the mother as a characteristic of the child. However, if you did not want to repeat, and just wanted the distribution of women who had a birth in the past five years, you could insert a line such as "keep if hidx==1" or do "tab v106 if hidx==1".
The KR file can definitely include more than one mother from the same household. They will have the same values of v001 and v002 (cluster and household id) but different values of v003. To get the distribution of the number of women per household who had at least one child in the past five years, use these lines:

* open a KR file
* instead of one record per child, reduce to one record per mother
keep if hidx==1
gen mothers_per_hh=1
collapse (sum) mothers_per_hh, by(v001 v002)
tab mothers_per_hh

For example, with the Nigeria 2013 survey, using NGKR6AFL.dta, I just got the following (unweighted) distribution. It shows that out of the 17,723 households that included at least one such mother, 87% had exactly one, 12% had two, and 1% had more than two, ranging up to a maximum of six.

mothers_per |
        _hh |      Freq.     Percent        Cum.
------------+-----------------------------------
          1 |     15,474       87.31       87.31
          2 |      2,053       11.58       98.89
          3 |        175        0.99       99.88
          4 |         19        0.11       99.99
          5 |          1        0.01       99.99
          6 |          1        0.01      100.00
------------+-----------------------------------
      Total |     17,723      100.00