Daughter started Play school but clingy

I wouldn't make her go. I have a feeling something about your break up with her dad created some fears in her that need addressing - mainly the possibility that you will break up with her (or that you are doing so each time you drop her at day school).
I would sit her on your lap and tell her that you will never ever leave her, and that you won't make her go to school until she is ready. There's no need yet for a lecture about kindergarten or even 6 months from now, because she can't think into the future that way. Tell her how happy you are that she made some little friends and how good it is to have friends to play with, because mommies aren't as good at playing when they are all grown up. Talk about those friends each day. Ask her if she will go one day a week just to see those friends and not lose touch with them. Ask her if it would be fun to have one of them over for afternoon play time, with her mommy.
If no amount of soft talking helps, take her to a therapist for 1 or 2 trial visits.

The crying stops most likely about 3 min after you are out of sight, and sorry but I have seen 1000's of mothers leaving kids at centers over the years, it starts out with mom's I will miss you , you be good, too much looking back and so on.

You take your child in, sign her in and walk away, not looking back. Sorry but I bet she is over it within minutes and off playing.

If she was crying the entire time she would not be making friends.

2 1/2 often just refuse to eat and are picky eaters, so they don't eat this meal, don't allow snacks and I bet they eat their next meal.
I have seen too many parents, the child is not eating meals, but they are given snacks between parents are not thinking about.

OMG,,, what makes u think m separated? when i mentioned she is not ready to go to her dad, i meant she want's no one but me,,, her dad and i are crazy about each other and nothing can separate us...

m sorry,,, i should have been more specific

Fr_Chuck,,, thank u,,, well, her teachers say she stops crying after a while,,, but starts once they take her out to play (that's where i drop her off), and doesn't stop until m there. i hope it stops soon.
every morning, as soon as she is up, she cries,,, i neither say yes, nor say no. i get her ready and leave her at the school gates and don look back.
my husband said he'l take care of her for an hour or two every morning, so that she learns to be away from me. do u think it's a good idea?

as for eating habits, i make sure i don't give her anything before/in-between meals. i treat her with a very small piece of chocolate, ONLY if she finishes her food. Some say it's a bad idea,,, bribing is not good,,, but if it helps me feed her, why not? i don bribe her to do everything.

She is a sweet kid,,, apart from eating, she does everything i ask her to, and no bribes....

It's hard for a child to see the big picture.
My son had trouble letting go of me the last few months (even though he goes to daycare for 4 years already).
Our daycare center has a development a specialist and she suggested we create a drop off book showing our routine from getting out of bed until I leave him at daycare. He drew picture for breakfast/brushing teeth/going to daycare/me reading him a story at daycare/ giving hugs and leaving. We put them in a folder and read it in the evening before he goes to sleep It really helped and he stopped crying and attaching to my leg after a week of this routine. You could make the book a little longer to include play time at the daycare and pick up. So she will always be reminded that they will go outside to the playground once without you being there.

Yes, smaller trips out with others for events helps

I've been here. My son was super clingy. I literally had to sneak out of the room during playschool, or the teachers would have to hold him, crying and screaming, while I made my escape. It ended with me crying all the way home, wondering if I was doing the right thing.

After a few months, when he realized that playschool was fun, and that I would be coming back, he settled in. I thought we were over the hurdle. We weren't.

In Kindergarten I once again had to sneak out, or have the teachers hold him while I left. He was always fine when I came to get him, loved school, but every morning it was the same thing. Once again a few months in he was fine.

Then grade one came along, and grade two. Same thing for the first few months of school.

It was hell.

I realized that a large part of the reason he cried was because of my reaction to it. It broke my heart, and I didn't hide it well.

In grade 3 I changed tactics. I took him to school the first few days, but registered him to take the bus. The first few days he cried, like usual, and I just gave him a hug, told him I'd see him after school, and walked away. When I went to pick him up I didn't acknowledge his behavior that morning, I just acted like I barely knew he was gone. Then he started taking the bus. We had a few hiccups with that, but after a week or so he got used to it, and after that it was all smooth sailing.

Instead of letting her cling to you when you're at home, go out, get your nails done, go shopping, or go for coffee with a friend. Leave her home with her daddy. Don't make a big deal about it, just say "I'm going out for a while, see you later".

The more you let her cling to you at home, the more you're around for her to cling to, the worse it will be. You have to allow her to separate from you a bit. To enjoy being with other people, and even being alone.

It's not easy, and there will be times where you will be crying more than she is, but it's necessary. It's time to cut the apron strings. Not sever, just a little cut.

My younger son would quiz me when he got home from preschool: "What did you do while I was gone?" and the kicker, "Did you have fun without me?"

I should have noticed that you wrote 'she refuses to go to her dad' and not 'her dad's.'
Sorry!