It took me a while to figure out just how I would write this...I'm a relatively blunt person, so I'll just say it straight out.
***Disclaimer: Prepare for straightforwardness.***
The way to stop this problem is to STOP enabling them. They are acting this way because you haven't put a stop to it. Now is the time, Momma...and it won't be easy.
I'm afraid that the reason your daughters are clingy is because you or another role-model in your home (or both of you) taught them to be that way...and you aren't helping matters by telling them where you are every second of the day.
You can show your love to your child without turning them into little leeches. It's called "teaching them boundaries."
You need to teach them how to be without you (and not molly-coddle them while you do it). Unfortunately, since it sounds like you've been coddling them for a while, it will be a hard road to go down. They are used to being able to act this way because it has always been allowed. Put your foot down and stop allowing it. Remember who the parents are!
Be tough. When you drop them off at preschool don't drag it out. Hug them and kiss them, let them know that you'll be back and they'll have lots of fun, and then leave. Don't keep standing there comforting them...even if they beg and cry. The first few times you will have to be stern with them, especially if they try to follow you. Don't be nicey-nice about it. You have to go, and they have to stay. Don't drag out the kisses and hugs. One kiss, one hug...goodbye. If this means leaving them in the arms of a caregiver...do it. Eventually the "drama-queen show" WILL stop and your child will be a more confident person.
If they cry, they cry. They'll get over it and learn that mommy DOES come back. I'm betting this will be harder on you than it is on them. Don't give in and don't give up. Don't show any anxiety in front of them...even if it means crying in your car by yourself when you leave.
At home you just need to put your foot down and be tough.
If you are busy, tell them. Kids are smart. Tell them how they can "help" you by going and doing their own thing...but make sure that you make it clear that it isn't a negotiation. You are TELLING them to go find something else to do. Let them know that you will not put up with them being underfoot every second. Give them a hug and a kiss and then banish them to their room, to an activity, or outside.
They do not need to know what you are doing or where you are in the house every second of the day. Just make sure that they get some of your time and attention after you are finished. Even if that means sticking your head in their room to admire their handiwork on a block building project before you move on to another task of your own.
Finally, I'm curious...are they in the same class? If so, it may be that they are feeding off eachothers fears and this is making it worse. I know they are twins...but the best thing you can do for them is to foster their individuality. They are two separate people and need to be recognized as such. Get them in separate classes and get them used to being away from eachother as well as you. Even if they beg to be together you must recognize that this is a crutch that they will not have in the future. They need to know what if feels like to be apart form you and eachother...and be comfortable with it. This will help you to cross a hurdle that you'll have to deal with when they get into "real" school.
I know this sounds tough...it is. You'll probably cry and feel guilty....don't give in. The results are WORTH it.
(**Especially when you realize that you can go to the bathroom without them freaking out about where you are.**)
Good luck! :o)
**Edit**
To the response above mine (I guess that is AFTER mine)...
Wow...talk about a guilt trip. Do you not realize that not everyone can be a SAHM? I totally respect those who are...good for them! But for some families it simply isn't possable! J. isn't a bad mom because she isn't staying home with her kids. And she isn't a bad mom because she sends her kids to preschool or classes (which shows them how to be confident, independent little people, btw!). Moms are capable of being fabulous parents no matter what they do for a job (being a SAHM is DEFINITELY a job! I've done it!). I respect your comment, but I think that the guilt trip that was inserted in it was innappropriate and unnecessary. What worked for you over 20 years ago is not always feasable for every parent today.
I hope I dont come across as too mean...I've not meant to be. I completely understand what it is like to be away from your children for a significant amount of time...the Army forces you to be away quite a bit. I feel for you completely. I really think it's just harder on your child if you don't teach them how to deal with your being gone in a realistic manner (I'm sorry...teaching your child to be dependent does NOT teach them independence...that is simply fallacy).
If all else fails, check out this amazing book all for kids about parents being away. It has a great activity that yoy might consider changing up to incorporate into your life:
http://www.amazon.com/exec/obidos/tg/detail/-/1557988064/...