If you’re a Prime member, you could set up a Family Vault with your mother, and then put the photos you want to share with her into the Family Vault. She can then view the Family Vault photos on her Echo Show.
If you don’t have a Prime membership, Prime Photos Groups might be an alternative for you; however, I’m uncertain if Groups photos can be seen on an Echo Show. I haven’t tested it out.
I too would like to be able to send photos to my mother. Someone suggested using the family vault but myself and I am sure many others are using Alexa as a way to contact family members who are elderly or have some degree of dementia and would be unable to go through the operating system or remember voice commands to access photos. My mum's Alexa 5 is on my network so I can set an individual background photo but I would love the ability to send a photo to her device and for the device to tell her she has a new photo and show it to her for a specified time. 30 seconds or a minute and then return to her original background.
Have you found a way round this? I'd love to be able to do this with my mum too. She has vascular dementia and I talk to her via drop-in. It would be great to be able to send her photos when I am out and about and show her what I am doing.