Welcome to the wonderful world of the potty, Joy!
Some things that I didn't see others pointing out were:
Girls and boys go to the bathroom at different ages. Girls start at about 2 1/2-3 yrs and boys at about 3-3 1/2 yrs. Those are average ages that I read about in Parents or Parenting magazines. It is something about brain development and when they are physically capable of this new skill.
Going to the bathroom is one thing that our kids have absolute control over. It does not matter how much we want them to do this. On top of them being aware of what their body is doing, they have to choose to follow it and sit on the potty/toilet.
Chin up! You are doing great, Mom! There is a light at the end of the tunnel! You are almost there! It is amazing how a little poop in the toilet can mean so much to us as a "parenting report card." I joked with my mother-in-law that I could only do so much and then it would just be his wife's problem. But, really, we all (or most all) get there before Kindergarten.
And, if their method of going very closely resembles a diaper change then they don't really learn anything. I learned the hard way with my son. He would pee in the toilet because standing and peeing was cool. He would poop in his undies and not tell me. I was not throwing out undies because of a little poop. I soaked/cleaned in the toilet. (Gloves were used) It became clear that even this was too much like a diaper change because I was the one doing everything. So, when he was 2 mos. shy of his 4th birthday, I started having him help clean the undies. He quickly decided that putting the poop into the toilet was way easier. (Within a few days)
Another key was that my husband and I were in agreement about the plan. We had the united front-there was no dividing/conquering to be had. That may have helped to nudge him in the right direction. Daddy took over much of the training after I pointed out that I couldn't stand and pee. My husband really stepped up for this and is still my hero!
My son is almost 8 and my daughter is 5. I've been blessed with kids who can go anywhere-not just home like I've heard about from friends. However, that means that even if we go before we leave home that we also go in a restaurant because they want to check out the bathroom. They could probably write a book on the ones they do or don't recommend. I also rememmber, fondly, when they would sing silly songs (they were in the stall) and entertain all the ladies in the ladies rooms. They have outgrown that. And, Daddy takes our son to the Men's room now. I don't think he sings in there.
I hope this helps to let you know that you aren't the first/last to deal with these things and that you know your child best and can see it through! This too, shall pass. (Pun intended)
D.