H.D.
Hi H.,
Having been a nanny that has worked in people's homes, here's what I found worked for me, and the children.
A Shut-Door policy: When the women I worked for were busy, they shut the door to their room or office. That shut door meant "I'm not here", so unless there was a serious injury or fire, our agreement was that they were doing their job and I was doing mine. This worked very, very well, although it's sometimes hard for the child to understand.
Nonetheless, when your au pair is "on", she's on. That means that when it comes to the your daughter's crying, refusing to eat or use the toilet, this is the au pair's turf. If these are attention-getting techniques as you say (it usually goes like this- child refuses to respond to au pair, au pair comes to you, helpless....or, it could be that you are working with one ear open and want to help out your au pair...), stop giving it attention.
In the case of not eating: leave a plate out for her with food that won't go bad after an hour or so. If she comes to the table and refuses to eat, don't make a battle of it. Tell your au pair not to push it and just to let your daughter go play or whatever else she wants to be doing. Trust me, she'll eat when she's hungry. No child ever starved themselves when they saw that no attention was being paid to digging their heels in and not eating.
In the case of not using the toilet: well, maybe she wets her pants, or messes them. If your daughter refuses to use the toilet, have the au pair work with you to help your daughter through this by letting her wet or mess and having your daughter help follow-through with the cleanup.
I don't want to say that you have to ignore her, but you do have to decide when you are working and you aren't. This needs to be clear-cut in your head and your daughter's head. Reasoning with a three year old may be difficult, but what you can do is set up a schedule so that you have two consistent breaks to visit with the kids, and keep those dates. If you do this every day for a couple weeks, your daughter will understand that mom is available at certain times, and she will be reassured. You will be able to get your work done.
One more thing, discuss this new arrangement with the au pair in advance, and not in front of your kids. I wouldn't blame, but be incredibly clear and communicate how you want the day to go and that you do not want interruptions due to attention-getting actions from your daughter. Review with her after a couple days and always keep these discussions private and away from your daughter. She will have to grow, and having it reviewed in her face won't help. Instead, with her, use empathetic language at the beginning and end of the day and avoid telling her that you've been listening to her cry and how it's affecting you. "I'm so glad to see you!" is a wonderful greeting.
I have more ideas but no more time...good luck and send me a message if you need to pick my brain. Like I said--I did it for years!