.....Often , she will unlock the car then spend a minute or two with the back door open whilst she fights the toddler to get her strapped in , When she then gets in through the drivers' door and goes to start the car , it does not start but sounds an internal beeping alarm .
It is called passive arming- If you unlock with the fob, and do not open a door within 30 seconds, the car will re-lock and the alarm and immobiliser will re-arm and will need the unlock button on the fob presing again.
If you unlock with the fob and only open a door other
than the drivers door, the immobiliser will automatically re-arm after a few minutes. It should normally disarm automatically when you isert the key in the ignition switch and turn it to position II, provided the fob is close to the ignition switch (ie. on the keyring with the ignition key. There is a ring around the ignition barrel which transmits a signal when the key is turned to position II, and this signal stimulates the fob to transmit the 'disarm' signal). Automatic disarming won't happen if more than one of the fobs for the car are close to the ignition barrrel at the time.
If the immobiliser doesn't automatically disarm, you should only need to press the un
lock button on the fob to transmit the signal to disarm. In this case, it may be that the ring around the ignition barrel is not functioning, or it may be that the SCU is not recieving the signal. As your fob buttons seem to work OK, I don't think the SCU reciever is being a problem (25s and ZRs with the Pektron SCU do sometimes suffer from water finding its way down the loom from the engine bay and getting into the SCU - the first thing that is comes into contact with is the radio reciever board for the fob signal, and you get no response from using the fob buttons at all).