I can understand your feelings. Maybe the way forward is for you to take control a little. On your days off why not pop round with a bunch of flowers, or chocolates , doughnuts, nothing expensive, just a little treat for a new mum.
Have a cuppa, and if baby is awake don't pick her up, but ask if you can give her a cuddle, but then leave so don't outstay your welcome. As you say goodbye, ask her if it's ok for you to pop round next week, if you have some, take some baby photos of your son with you.
But keep the visits short then after a few weeks perhaps you meet up with her mum and you for a coffee in town.
It's normal that daughters will automatically reach out to their own mums , just don't push too hard, make visits a regular so that they become a habit, when baby is a little older your DIL may like to visit the shops with her own mum while you babysit just don't push too hard