I, too, like to include secondary cities in my itineraries, but nine nights for Helsinki, Tallinn and Riga doesn't leave much elbow room as far as I'm concerned. You have to consider how many hours you are giving up in the capital city in order to have far fewer hours at the side-trip destination. In addition to the travel required, in many cases you need to allow time to get from your hotel to wherever you've managed to park your car. (If you stay outside the center in a place that offers parking, you'll waste an equivalent amount of time getting from your lodgings to the tourist sights in your base city every day.)
I'm someone who suffers greatly from jetlag and sleep-deprivation after an overnight flight to Europe. For me, this is an 8-day trip, and there's no way I'd want to add additional stops beyond the three originally mentioned. However, I am all-in on art, decorative art, 20th-century history and interesting architecture. Those with fewer, or less in-depth, interests may be fine with less time in each city.
Turku and Kotka are each about a 4-hour roundtrip from Helsinki (once you've retrieved your car). I haven't been to Kotka. Turku is an interesting place with some good museums, but unless the Aboa Vetus archaeological museum is a powerful draw for you (Turku's much older than Helsinki), Turku pales in comparison to the capital.
Suomenlinna is a sea fortress you reach by ferry. I don't know how long that ferry takes or how frequently it runs. The sights out at Suomenlinna are scattered; it would take a good bit of time to see a few of them unless you chose your targets based solely on proximity rather than interest. I haven't been out there myself due to lack of time.
I haven't been to Sigulda.
Two of us have given Kaunas high marks, but it is a 7-hour round trip from Riga. In the context of your trip, I think it is not a good idea.
I've already given my opinion on Parnu; it's totally skippable.
A quick look at Google Maps tells me you could include a detour to Tartu on your way from Tallinn to Riga at a cost of about 1-1/2 hours of extra driving. That's not a major time expenditure, but I'd think carefully about what I actually planned to do in Tartu and whether it is worth cutting into your Riga time. You have only two days in that city.
I did not remotely cover the full expanse of Estonia and Latvia, but my general comment is that a lot of the scenery is far from spectacular. This is not Switzerland; the journey isn't always visually exciting.
In case you haven't seen them, these are Rick's sightseeing tips for Tallin: https://www.ricksteves.com/europe/estonia/tallinn (Click on "At a Glance")
And this is what he lists for Helsinki: https://www.ricksteves.com/europe/finland/helsinki (Click on "At a Glance")
I do not recommend the Helsinki City Museum unless the traveler has a great deal of time in the city.