Just a copy/paste from a nice article on the subject found HERE
Avigdor Shinan introduces “Eishet Chayil” in the Siddur that he edited
and annotated, as follows: This biblical passage has been included in
the Siddur since the 17th century (when Kabbalists established other
portions of the Friday night liturgy, such as poem Lecha Dodi—jb). Its
recitation on Friday evening is interpreted alternately as referring
to Shabbat, the Tora, or the Divine Presence, and it describes the
Sephira of Malchut according to the Kabbalists. Nevertheless, many
today understand it as a song of praise and thanks that the members of
the family sing in honor of the matriarch of the home for all that she
does during the week in general, and what she has done getting ready
for Shabbat in particular.
Assuming that singing Ashet Chayil does not trigger any unpleasant feelings for his wife, then there is no problem singing it as the passage is a allegory (indeed the source for Ashet Chayil is in the book of Mishlei) as mentioned above and verses like "her children rise up" can be interpreted on a deeper level.
I encourage you to read the whole article to get a deeper understanding of Ashet Chayil