How detailed would you like your answers to be?
For the peacocks, it’s more important for you to be trusted by them. A good way to test this out is to let them decide if they want to go with the Grovers, or stay with you. If Orlando and co. did the latter, you’ll have a better chance of winning the contest.
You get the most opportunities to becoming friendlier with them in chapter 4 after helping Valentine with setting the table and in chapter 7 while taking a walk and ignoring both Mopsie’s and Regina’s plans, and meeting with Frankincense at the gazebo later that night. For the latter you need to set up a meeting with them first though.
If you plan on getting away with cheating (and, from what you said, I’m guessing you had to wear the “I Cheat at Exotic Animal Shows” sign?), make sure your Skullduggery is one of your better stats. Choosing to be a thief as part of your backstory will also make things easier.
It’s been a while, but I don’t recall anything else from the animal show that can affect the boat rowing event. Again, the most generic help I can give you is to play to your higher stats.
Also, always pick the longest and most dangerous path, but that’s a personal choice.
Statswise, I would suggest picking 1 stat you want to leave behind and raising the other 5. I find Culture and Skullduggery to be the easiest ones to pick. Things should be less unstable then.