to install the software on both your PC and your laptop, as has already been stated. However, the laptop must be a machine that is owned and used by the same person who uses the PC, and that - as ßéLâ advises, would not be the case here.
I see from your phone-call scenario that your daughter must know both of mine.
with Office 2003 [Or Office 11 as its known] this has been expanded to three PC's, desktop,laptop or any combination of the three and can be used at the same time but must be close members of the same family living at the same address.
I think that you would not get a knock on the door if your son/daughter was staying at uni. as long as her home address is still the same as yours.
Only with Office 2003 would this apply. Other versions are as FE states. 1 desktop, 1 laptop owned by the same person and used by the same person but not at the same time.
If you have a desktop and laptop in your home that belongs to you then you may install Office to both of them, I don't think for one moment you will get into trouble for it, there is no way of checking, but to stay within the EULA you should use only one machine at a time.