score:4
There are no advantages I can think of in ordering it online. Every hotel and every tout in Rome sells those (and some will even deliver the actual pass).
It depends on whether your kid is EU citizen. Some museums offer substantial discounts or even free entry for kids, but only for EU citizens. Other museums (i.e. Vatican museum) offer discounts for all kids, not just EU, but it is not covered with the pass.
You need to list the museums you plan to visit and see whether the discount offered pays for itself. Note that many attractions (i.e. Pantheon, Trevi Fountain, St Peter) are free, and it is possible to spend three days in Rome without spending a dime on sightseeing. Other attractions, which are not free, may not be covered by the pass (Vatican Museum is not covered).
So please make sure the pass is a good value, and pays for itself. Keep in mind that "skip the line" has little value as tickets to most museums (i.e. Colliseum + Forum - a single ticket for 2 days) can be booked online. And the longest lines nowadays are security lines which you can't skip. Free public transport access is also of a little value, as the attractions are pretty close and the city is walkable. I just got back from Rome, and in two days I never used any public transport there except 14 EUR Leonardo Express to/from airport (and this is NOT covered by the Roma pass).