Many posters have offered helpful insight & suggestions.
A few stand outs are:
You have got on well with your DiL, in these sleep deprived times of major adjustments, your DiL will understandably turn to her own parents for familiar comfort. Which is not to say that you cannot offer support & care, but it’s an immediate reflex intimacy to turn to your mum & dad for comfort & support.
Although you are invited, ease back a bit, get back into your own routine & pay attention to things that matter to you & bring you joy. Be less available, give them space & when you see them, be fabulous. Just let them miss you a bit.
It’s good idea to speak with your DS to find out how they are each are doing, offer support & ask what you can do. Be honest with him how you’d love to have a cuddle with baby as you did have such lovely cuddles with him at that age, but you realise that things are different when it is not your own baby. Share with him stories of your own experiences – it might help if his father chipped in with early Dad recollections, maybe even get out the baby pics. Keep this all very light & chatty, make it easy for them to share more with you as their lives open up.
Agree about the perfum.
You are used to it & may not appreciate how it lingers.
When the fog of early parenting lifts, they’ll remember what life was life & parents who baby sit or offer respite enough for a hot bath/nap/ read a book will be most welcome.