Try to pick direct train for Katra.
Book online Yatra Parchi.
Book hotel in Shrine Board's bhavan.
Take new route for Ardhakumari.
You will enjoy the route and its beauty From Banganga you will have facility for baby take care on chargeable basis.
Battery Motors from Ardhakumari (Rs 354/ per person) to Bhavan. It will take 15 minutes.
I would say this is the best time to visit vaishnodevi mandir because its less crowdy in these days and the weather would be very pleasant plus i would recommend you to start you walk in the noon time so that you can reach the bhawan by 9 pm and then you should go for darshan at around 12pm why i am saying this because after 11pm they open the holy gufa of mata vaishno which people think is closed for pilgrims so try to do the darahan around 11pm and yes dont forget to carry clothes as warm as possible because its going to be very very cold up there. jai mata di !!