I am an active member of a Reform congregation and know a lot of converts through that channel. In addition, I've taken some training (from CCAR/HUC) designed to prepare lay people to assist with common synagogue tasks ("para-rabbinic", of a sort), and this training included conversion assistance. (Note: lay people do not make decisions in that area; that's the prerogative of rabbis. But I've helped teach classes, for instance.)
The CCAR (Central Conference of American Rabbis, the governing body of Reform rabbis in North America) does not require that existing children convert along with the parent, but does require discussion of the matter. CCAR does require a commitment that future children will be raised Jewish. Some rabbis amend the required pledge to say "exclusively Jewish", though that's not in the CCAR guidelines for rabbis. According to the rabbi who taught my class, "exclusively" is clearly the intent, and goes with the commitment to have a Jewish home. (Note: it looks like the copy on that web site is missing embedded Hebrew. I have a paper copy.)
To quote from that document:
f. discuss with the prospective ger the religious status of any current children and if there is a necessity for them to be included in the process of exploring geirut.
When both parties are active participants in the process, issues of lack of partner's support, or outright opposition to can be discussed and solutions can be found far more effectively and far earlier in the process. [...]
1f. If the prospective ger has children the following questions should be asked and discussed: What is their status? Are they Jewish according to Orthodox halakhic standards? Are they Jewish by Reform standards? Are they not Jewish at all? If not, is it appropriate for them to become involved in the process of geirut, and if so, when? Should they participate with their parents or should these issues wait until their parent(s) are clearer about their own intentions?
This leaves open the possibility that such children will not convert. I don't see any age-based discussion here; that seems to be left to rabbinic discretion. (I can imagine that a teen leaving for college soon might be treated differently than an infant in this regard.)
The requirement about future children is in the boxed text in the section called "readiness".
See also: CCAR Responsa: Conversion of a Young Child of a First Marriage:
In summary, we urge that a complete conversion take place for the young individual if it is agreeable to both parents, and then insist that the youngster be provided with a Jewish education.
This responsum cites Shulhan Arukh Yoreh Deah 468.7 for a child being able to reject a conversion at the age of bar/bat mitzvah.
As noted above, the CCAR is the North American rabbinic body, so it's possible that rabbis in other parts of the world follow different requirements. In practice, though, I've never heard anybody mention another Reform rabbinic body; I suspect policies elsewhere won't vary on this point.