In general, and not just on laptops, audio systems which are designed to work with both loud speakers and headphones incorporate a switch in the headphone socket to disable the speakers when headphones are plugged in. This normally works by a contact which is pushed out of the way as the headphone jack is plugged in, and like all switches can fail.
If this is the case here, then it is a hardware problem and not a software one. A brief spray of switch cleaner into the headphone jack followed by several rapid insertions of the headphone jack might resolve the problem. If you can't get switch cleaner in outer space then a drop of iso-propyl alchohol will do just about as well.
If that doesn't work and the laptop is out of warranty, then depending on how annoying to everybody else the problem is, then you may need to consider getting more drastic. The first approach would be to think about replacing the headphome socket. this would require (1) dismantling the laptop, and (2) being able to source a replacement. I would have a look on YouTube for videos on how to dismantle your model of laptop before I went down this route.
Another approach, assuming the laptop is well out of warranty, would be to install some sort of kill switch on the feed to the speakers. This would also require dismantling the laptop, some expertise with a soldering iron, the willingness to drill a smallish hole in the laptop case and a suitable miniature DPST (double pole, single throw) switch.
I can understand how annoying this can be - there you are trying to listen to some contemplative piece of music on your hi-fi, with the sounds of Angry Birds in the background ! Lowering the volume on the laptop won't improve things either because the one volume control affects both speakers and headphones. Turning the volume down would mean that your daughter can't hear her instructions. Looking on the bright side, it does mean she can't get away with Angry Birds - or whatever is her fancy - when she is supposed to be doing her homework !