3 yr old daughter pooping once in 3 days. Please advice.

My 3 year old daughter poops only once in 3 or 4 days. She eats really well. I even give her banana smashed with cornflakes and milk every day. She eats 4 times a day and good quantity of food with vegetables and brown rice. I tried to potty train her in her toy potty. From that day she hates to poop at all. Now i relaxed her and told her she can poop in her diaper or panty what ever she is wearing. But still she tries to hold the poop and hesitates totally. This is happening for the past one month. She drinks enough water also and has good physical activity too. When i asked the doctor, She said feed her in a way that she cant control to hold the poop. I am feeding as much as i can. But my DD is stubborn and hates pooping. I even rewarded her and keep encouraging her but she is just not falling into routine. Everyday i have to eagerly wait if she will poop or not. Otherwise she is happy to say when she wants to pee and she straight away go to the potty for peeing.
Anybody experience this peculiar behaviour. I really hope this is a phase and it will over soon.
Please advice.

 

Thanks for the advices!
She takes only home made food. No junk snack at all. She hates apple and guava. I cant force feed her. I even gave dry grapes juice for her daily. I am talking with her and even congratulating her once she poops. Sometimes she is so stubborn. I just want her to make it a practice of once a day. She hardly take any milk at all only with cornflakes.

 

Thanks for all the advices!
I tried what ever you have mentioned.
My primary problem is my dd has to poop first. Pooping in the potty is the secondary problem. I mixed prunes in the chutney since she refused to eat the prunes as such. I tried massaging her stomach. It didnt work.
Her daily diet

9.30 - toast/idli/dosa/uppuma/poha - (given in school -she eats well)
12.30 - one cup of sambar rice, one cup of curd rice and any vegetable kootu
4 - one cup of cornflakes with one mashed banana with milk / one cup of popcorn
7.30 - 3 brown rice dosas with chutney / 2 chapatis with subji

10.30 - one small bowl of cornflakes with banana with milk (If she is awake till 10.30 and asks for cornflakes)

Finally we went to doctor today.The doctor advised to introduce oranges and pomegranates in daily diet. I was worried if it might cause cold or fever in this climate. But he said it was ok even if she gets cold and i could just add cold syrups.
He has also prescribed "Cremafin" syrup which is a laxative.

Keeping my fingers crossed. Nowadays i am finding myself in a very irritated mood because of this constant problem. I am so worried what if toxins are produced in her stomach with all the poop.

My DH keep saying this is not a big issue at all and he had the same psychological hesitation and hatred to poop when he was young (till -10yrs). Hmmm...looks like this typical gene has been transferred from my DH to my DD.