Brief summary: I recommend a rear seat with suspension for speed and safety.
You can definitely train effectively while hauling your wee one. We have a 3.5yo and currently own a Thule (Chariot) Cheetah 1 (two-wheeled trailer), Weehoo Igo Turbo (single wheel recumbent pedal trailer), Hamax Caress (rear seat), and Bellelli Pepe (rear seat) for hauling her around. The key to getting out for a ride is that the passenger is comfortable and cooperative. We sometimes offer special snacks, stops at playgrounds, and even ice pops or ice cream to get out for a ride.
Your training requires that you do good workouts, presumably with some kind of training plan. I highly recommend using a power meter or heart rate monitor for workouts with your child in tow. You'll be going a lot slower than you would without your "helper", so you'll want feedback that helps you to do your workout.
As for safety, there's very little evidence that any method of transporting a 2yo is better than another. It is really important that she's dressed appropriately for the wind and weather (you'll dress like a cyclist, but she'll need to dress like a motorcyclist). It is really important that she wears a helmet if she's not enclosed and buckled. It is really important that you're visible (front/rear flashing lights, fluorescent colors, flag). It's also a good idea to choose safe routes for towing her around.
We like the two-wheeled trailer for paved routes only. We use the rear seats for non-paved routes that have much less traffic. The rear seats are significantly less cumbersome to ride with than either of our trailers. I feel like the Weehoo is the most cumbersome option.
I've also rolled the two-wheel trailer once. We were cornering at speed, and I swerved mid-corner to avoid roadkill. My rear tire hit the trailer arm, instantly flipping the trailer. It woke my daughter from her nap, and she wasn't pleased about that. She was wearing the 5-point harness in the trailer and wasn't injured or traumatized to my knowledge.