The reason they are 'sick' is because they are anxious- mum is out and they are a bit worried that they are isolated with a non-mum. You can't deal with them the same as if it were your own child, so the best thing to do is say 'oh dear! I wonder what could be wrong?' do lots of fake 'tests' on them for temperature, look in their throat, etc (nothing below the waist though!). Say 'ooh I think you'd better stay lying down in bed - I'll stay with you and read you stories till Mummy comes home' and then do just that. Mummy would probably rather come home to find an awake and happy kid than an awake and scared kid.
Just tell them that if they keep on saying that they are sick, they will be really sick and if they are sick they will miss out a lot of happenings like going to the carnival, playing with their playmates and of course they will be stuck in their room with their medicines that they have to take in..well, as we all know children hates its taste..
My Mother and I relied heavily on the old rocking chair. If that doesn't work try putting them in their car seat and driving, of course warm up the car and take necessary gear just in case, but driving puts most young children to sleep.
Give it Motrain it will make the child feel better and put the child to sleep
I'm taking my 4 year old daughter to counseling. I've tried tough love, nasty medicine, visits to the doctor, and love. She wears it all like a badge of honor. She can put out some tears and fake nausea so well that she has had her best friend and teachers convinced. I've had the principal put my daughter back in the car because "She's too sick to be here today." She's a supreme faker. During the day, she will ask, "is school over yet?" If I say yes, the skipping and laughing commence. If I say no, I get a groan. So we're headed to a child psychologist.
Give lot of love, attention and quiet time and a little medicine won't hurt
Let her do what she wants then after a while she'll get sick of it and give up .