Pick 2 simple phrases that you are comfortable with and then don't deviate from them for 2 years.
In my case, I picked
1. "we are moving to live with Grandma for a while. I know you miss Daddy. He misses you too. Mommy and Daddy decided this is what was best for everyone"
2. I know it's hard to not have all your stuff. We have the important stuff, and the other stuff is safe." (for us it was in storage).
3 years old is both super tough and much easier. In a year she won't remember the two of you living together. Which will make it less easy for her to envision that you would get back together one day. But 3 is tough because she will never have those memories. So, it's a double edged sword - as divorce tends to be.
If you have a specific date that he will see her.... always end your "phrase" with that...... I know it's hard..........blah blah...... but you will see Daddy on Thursday, remember?" That will give her a specific date that is more concrete so things don't seem so up in the air. If you DON'T have a date, no worries.... but refrain from saying things like "I don't know when...." because that will make her feel like things are secure.
For myself.... I either bypassed it entirely with re-direction or I said "that is up to your dad and I hope that he will make plans, but right now we are living with grandma......." and went right into the previously aforementioned schpeel.
I also found it helpful to NOT explain things. That's not for her to understand. I only told her what I knew for certain and only if it related to HER world. Here is where you will live, this is what time you go to bed. Here is where you go to school. And less on "what I think we may do....." It's easy to want to provide info.... but with a kid that young they can't process info and time is still relative to them..... so giving info that will happen in the future will sometimes confuse them more.
Above all - you have to simply ignore all the judgement. It will come at you from everywhere and most times when you aren't expecting it. A teacher, a bank teller, a responder on an advice board. Everyone thinks your shoes are more comfortable and your grass is greener so you should have stayed or done this or that. You have to answer to you, your daughter and whatever higher power you believe in. That's all.