Hi C. L,
I don't know if this will be helpful for you or not, but my daughter was the same way at 3...she would go pee pee, but not poo poo. We ended up telling her that she could have a "Poo Poo Party" with whatever balloons, cake, her favorite colored streamers and theme she wanted if she poo pooed on the potty...(tell everybody right away of the exciting news...or have her tell everybody if she can...family, etc. and let them know she is having her special poo poo party to celebrate...whenever convenient to you!)
The first time, I saw her sitting there and starting to go and I picked her up, pulled her pants down and placed her on the potty...needs special timing for that which one doesn't always have! We sat with her and when we saw she pooped, we both cheered like crazy and told her that we could now have the party!!!
Well, we did but she was afraid again to poop (not really her idea since I put her on there). So, my hubby promised her roller skates if she poo pooed on the potty and another party (it was with just the three of us..small to-do).
One day, not long after the first party, I was about to change her diaper and she said to me, "No, mommy. I want to get roller skates...I am going to go potty" and just like that, on her own, she went into the bathroom and pooped! When I got in there, she said, "That wasn't scary"...I guess she was feeling like it was a "scary" thing to do? Anyway, we made a huge hip hip horray deal about it and called everyone again, ordered the skates and had the "Official" Poo Poo Party again that weekend (with the leftover plates, etc. from the first and new balloons)...she even wore a party dress and I took pictures.
SO...that is what worked for us and we have not had an accident yet in bed or out. She just decided when she was ready. We don't make a huge habit of giving her "stuff" rewards, but since this was a big milestone, we did and she loved the parties.
Might be helpful? Not sure, but we were concerned too with our little one and she just did it when SHE chose to, we just gave her something to look forward to if/WHEN she did.
Good Luck!
E. E. and Maddie