My daughter is turning 3 in November (a fact that she reminds me of daily ... smile). She too is very very clingy to me right now and is very detatched with her father too. She will actaully tell him to "go away" when he tries to interact with her when she's with me. She would even rather stay home with me than go to the park with her Daddy ... (strange) I think it's a stage of their age and we just need to give them as much time, praise, attention as we can ... without us going insane. It is perfectly ok to need a break from her too. If you find youself needing a break away from her I would tell her that you need to go do ... (whatever) and that she is staying with her Daddy and they are going to have fun doing (talk with your husband about doing something she really likes). Even when she whines, cries, and hangs on to you... make sure that you go. She will have a good time with her Daddy, you get that time to yourself and she learns that sometimes we don't get what we want. (smile... the hard lesson of life).
Feel free to message me if you want some support. I am frustrated as well at times with this... but then there are times like when we cuddle up together to watch a movie or something and things just seem right. Hold on to these moments because I am thinking... they won't last that long.