How can I make sure my kids aren’t seeing my photos on their phones?
If all photos are stored to the iCloud, how can I make sure my photos aren’t showing up in my kids’ photo libraries besides checking their phones. I have grown children.
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If your kids don't know your Apple ID password (i.e., they have their own Apple ID) and you aren't sharing your photos (as described in How to use iCloud Shared Photo Library - Apple Support or How to use iCloud Shared Photo Library - Apple Support ) then they wouldn't have access to your photos.
That is true even if you are sharing an iCloud storage plan. See the following from Share iCloud+ with your family - Apple Support
When you share an iCloud+ subscription, everyone in the family group uses their own account. That way your photos, documents, and other information stay private, even though you're sharing access to the service. You simply share the features and space available in iCloud+ with your family members, so you only have one plan to manage.