First of all, the fewer connections, the better. Each connection means pulling a sleeping child off the plane, losing luggage and possible delays. Also, with airport taxes, it's probably cheaper to book with one connection anyway.
Having said that, I would go with whichever is cheapest! Make sure the business class doesn't have a "fishtail" design or other configuration which would make it difficult to take care of your little one.
My children were very active and didn't like to sit in strollers or car seats. It was a g-dsend to have the car seat on board though. I could slip them in it when they fell asleep and was able to get up, use the restroom, etc. I rarely had the luxury of flying with my husband.
Thai is a bit vague about which car seats are allowed in the cabin. You may want to contact them (by email) before you book.
http://www.thaiairwaysusa.com/flight...e-you-fly.html
This is a tough age for travel. Be prepared to do a lot of "aisle laps" with her and bring plenty to keep her occupied. If you go for business, don't hesitate to take her to walk in economy if the aisles are free. In fact, if you do sit up there, try to seat yourselves towards the back of the cabin, both to have access to the restrooms and be able to get up. You'll also have fewer other passengers staring at you.
Some might suggest drugs. I've seen it done and a couple of times, the child has had the opposite reaction. Talk to your ped and make sure she's tried whatever you give her before. Also ask what dosage (since most drugs work stronger in the air, don't give her the full amount).
Be sure to have a good baby carrier as she might get clingy and/or too tired to walk in the airport. A soft front/back pack would be best. At that age, I put the car seat on a metal luggage cart, secured it with an extra bungee and that was my "stroller" when she couldn't walk anymore. Less to drag along. I'd either check or borrow a stroller at my destination.
Bring way more diapers than she usually uses in this time frame, changes of clothes and plenty of snacks (don't expect her to eat when and what is served). Please let her sleep on take-off and landing. It's a myth that they have to suck on something. Schedule a ped visit right before leaving so that you're sure her ears are clear and healthy and she'll be fine with the pressurization changes. Don't wake her unnecessarily.