Underground Colosseum Tour with kid

A month ago I stayed in the Hotel Lancelot on Via Capo d'Africa: https://www.lancelothotel.com/ . It's three blocks from the Colosseum. And it's a great hotel for independent travelers.

The underground tour idea is excellent if there is one.

We booked the tour through Co-op Culture, the official site. https://www.coopculture.it/en/products/full-experience-ticket-with-access-to-the-arena-and-underground-of-the-colosseum/

This can be challenging, as it is a popular tour, and the tour companies grab up most of the tickets quickly. However, if you book through another tour company, you essentially pay more for the exact same thing, so it's worth it to try. Tickets go on sale 30 days ahead of the date you want, at ~9:00 am (I think), Rome time and can sell out in minutes for busy dates. If you miss it, you can try to book through a another tour company, such as The Roman Guy.

Just to add, you cannot access the underground without a tour, either Coopculture's or an outside company's.

Along with the link for the Coopculture tour provided above, there is this one:
https://www.coopculture.it/en/products/the-wonders-of-the-colosseum-visiting-the-underground-and-the-arena/

It provides guide service not just for the underground but for other parts of the arena as well.
Yes, Coopculture tours are in high demand because of their economical price so those reservations can be difficult to land! Even the outside tour companies themselves are finding it difficult to get their hands on reservations; we've seen any number of posts about last-minute cancellations from people who booked with some of them.

I did a tour of the colosseum and the palatine hill, including the underground, with Livitaly tours. They were very good as they are all historians.

These tickets are very hard to get. Many tour companies don’t even try to sell them anymore. Others, cancel at last moment because they don’t have tickets.