alternate or alternative?

When do we use alternate and when do we use alternative?

We use ‘alternate’ or ‘alternately’ to mean ‘every second one of something’, or ‘in turns’. But ‘alternative’ or ‘alternatively’ is similar in meaning to ‘different’, ‘instead’ or ‘on the other hand.’

Compare:

My daughter spends alternate weekends with her grandparents.

Sorry I won’t be available on the 27^th. Can you find an alternative date?