I’ve sent several text and voice messages to my daughter with no reply. Is it possible that her husband has a way to receive these messages and delete them before she sees them?
Well, yes if her husband has her iPhone and knows her pass code (if one is set) - he could ofcourse review and delete any messages before showing them to your daughter.
If her husband knows her iCloud account details (including password), he could setup iMessage on a Mac or another iOS device to receive copies of messages to review. However, deleting those message on his device won't delete them from her device.