How can I get my 3 year old daughter to poop on the potty?

My 3 year old daughter has Mosaic Down Syndrome.  It hasn't effected her very much.  For the most part, she is developing at or above average.  She was even released from special education services.  However, they did inform me that she is about 6 months delayed in some cognitive skills.  Aparently, this is not a significant enough delay to require special education.  Anyway, we introduced the potty chair to her at 18 months because we had planned on trying to potty train around 2 years if she was ready.  She went pee on the potty just about every night before her bath.  When she turned 2, I was about to deliver my second child, so I put off potty training because I knew children typically regressed after a sibling.  I started trying at about 2 1/2, but she wanted nothing to do with the potty at that point, so I waited again.  She just turned 3 and is going pee on the potty pretty regularly.  Sometimes she will go on her own.  Other times I have to ask her to try.  She really wants to wear underwear, but I honestly do not want to keep cleaning poop out of them.  I keep telling her that if she goes poop on the potty, then she can wear the underwear.  She is not constipated.  I've tried putting her on the potty when I know she's due to poop, but she won't.  I'll let her sit up to 20 minutes, but she won't go.  Then, sometimes as quickly as 5-10 minutes later, she'll poop in her pull up.  She will often let us know when she has gone so she can be changed, but just won't go on the potty.  She has gone on the potty 3 times in the last year.  We've always praised her for doing so and don't punish her for not going.  I've got special rewards for her if she goes that are in her sight.  I just don't know what else to do.  I don't know if there is a delay due to her having Mosaic Down Syndrome, or if this is just something many mom's go through.  I would appreciate any advise.  Thanks.

[tiredbuthappy]

i don't know if her problem is specific to her condition. i did want to let you know that this is VERY common for young children. i've worked with typically developing children who were pee trained at 3 and not poop trained til 4. if i had to guess, i'd say almost half of the kids i've helped potty train got the poop thing down after the pee thing. as many as 1 in 10 took a VERY long time to get the poop thing down- several months or even up to a year.
the only compromise i can think of is to teach her to ask for a diaper when she's ready to poop. it's better to change one diaper a day than a poop accident a day. to help work towards being totally trained, you can put the diaper on her and ask her to use it while in the bathroom to help reinforce the idea that we poop in the bathroom.
i worked with one family that had a similar problem for a long time. letting the girl ask for a diaper reduced everyone's stress. to get out of the habit, they started having her sit on the potty while wearing the diaper to get her comfortable with that. then, one day they cut a hole in the diaper before putting it on her. when she pooped, it fell in the toilet. after seeing that she was OK, she no longer had that problem.