I think your heart is completely in the right place but you maybe need to communicate your ideas positively in order to get the right result.
I would firstly not raise DS's hopes (if he is lonely and would want to see them) by telling him GP are visiting his student town for a day trip, if they have no intention of including him. I would speak nicely to PIL to explain that you are wondering if DS is finding the first few weekends hard by himself, as experience from the past tells you there's a chance he could be, and if they are willing then offering to include him, the forthcoming trip might be a very welcome invitation for him. And you will pay/settle up with them. (you've mentioned you think they might not want to pay for him so just offer regardless of any rights or wrongs over it to bung them £20 or £30 for lunch and entry and whatever, it's worth it surely just to get the money issue out of the way if that's a factor).
If they make it clear they don't want to include DS on their trip or even see him without it being grudging and coming across as such, then you have to weigh up chances of him finding out, whether he would be happy with a 4pm visit rather than the offer of the whole day out etc. If he could find out they'd been without mentioning it to him then he needs to know they are coming. But ideally you'd appeal to their better nature/grandparently love to include DS and help them empathise on how he might be feeling, whilst still acknowledging that DS might have an offer to go out with some new pals so if so, they won't be offended or make it obvious to him they are.
Then you can present (or let them present) DS with their visit idea, ideally a choice of whole day trip or 4pm visit if he doesn't have other plans. (at this stage if he has a chance of invitation with new pals he should definitely take it without feeling guilty about turning GP down, as it's the early weeks when some people are in the same boat that bonds are made and friendships are formed).
It could be your DS would be happy with just a 4pm visit, or actually doesn't mind not meeting up with them this time, you don't know. Ideally they would offer him the choice of joining them on the trip or a 4pm visit.
Some GPs need a little push in the right direction, they can be a bit thoughtless and find it hard to empathise somehow even if they are loving. If they are generally good GPs then I would just make try to make things happen in as positive a way as possible (and whinge behind the scenes to your friends or on MN) 