We would like to walk from the Colosseum to Altar of the Fatherland, Capitoline Hill, Mouth of the Truth. Then take a taxi back to Piazza Navona.
You've got the order right, starting at the the Coliseum. No, the "Mouth of Truth' is not really worth it. I've been there multiple times years ago, not that interesting unless perhaps you're a super Roman Holiday fan?? I would walk down the Roman Forum (preferably later in the day) & take the short cut on your left up to the Capitoline Museum, (you will see people walking up the hill). Unless you want to pay to ride lift to the top of the Wedding Cake (Altar of the Fatherland) for the view out over the Forum, I would skip going into it, just go to the much more interesting Capitoline Museum piazza. You can then turn left to see the view out overlooking the forum from the veranda, VERY worthwhile! (walking slightly downhill to your left between the 2 the museums to the viewpoint.) There is a taxi stand down the stairs of the Capitoline Museum to your right on the big square, it's moved a few times due to construction but it's there. That would get you back to Piazza Navona.
OR continue walking to the much more interesting gem across the road from the Mouth of Truth, Teatro Marcello, which you can then walk through to the gorgeous Porto Di Otavia, at the beginning of the Jewish Ghetto. But that's more walking. Stopping for dinner (except on Saturday after sundown) in the Jewish Ghetto would be fun, then ask the restaurant to call you a taxi. Enjoy!