It seems your family isn't confident in using high-speed trains, so they hesitated to act without you. Many older people are reluctant to ask for help. It's best to guide them like children.
It feels like the kind of place that's perfect for leisurely strolling. It's not really for those who just snap a photo and leave, because there's just too much to see to rush through it.
I've been here for seven years, and I'm not used to it either. It's freezing cold in winter, boiling hot in summer, and I inevitably get prickly heat every summer.
The essence of Hangzhou is about enriching your spirit and enjoying the scenery. It's not suited for a whirlwind, 'checklist-style' tour; you really need to take it slow to fully experience it.