Instead of sharing password of your gmail account, you can easilty setup email delegation by which the delegated user can access same email account with his primary gmail login.
Refer How to Set up mail delegation in Gmail.
By default, delegated account will not be able to access from mobile apps but you can achive this using a mobile browser.
Open gmail.com in Chrome or Firefox
Tap on Setting bar on left top.
Request Desktop Site
Open Settings and Choose Gmail Desktop
Scroll to bottom and Choose Desktop
.
Switch to Standard View
Gmail Desktop will open classic gmail (html) desktop version.
Scroll to bottom and Choose Standard
.
Access Delegated Account
Tap on your profile picture and see all accounts you are already login.
Scroll down find all those delegated accounts you have access.