Learn English – “You could do worse than [x]”

In this context, the phrase "separated at birth" refers specifically to twins. It was not uncommon for twins to be separated at birth or a very young age in earlier times - especially in adoption cases, where one child would be picked up and the other left behind, etc. As fate would have it, many twins [have] rediscovered each other (and continue to do so). Many of these stories have captured the imagination of the public and attained a special degree of sensationalism.

Thus, separated at birth has grown into popular culture as a joke one uses when they meet someone that appears to share their traits, either physical or otherwise.

The phrase is correct, just unusual. People use it to be unique, and to make mundane questions like "how are you today" become a little more interesting. And clearly it worked, since you asked this question.

Don't discourage your mom from saying this phrase. It's good that people use phrases like this, because it makes a question that should truly be asked wholeheartedly stand out more. I don't really give the question "how's your day going?" much thought. I just automatically say "fine". But a phrase like "how's your today?" turns on the thinking machine, and my answer is sincere. It's also a much more lighthearted approach to the daily question.

I know I did a lot more than answering your core question, with a lot of opinion-based stuff, but I actually think it's something one should consider. Using sprighty and unusual phrases instead of the grey, mundane and regular phrases we've become so accustomed to. Give it a try.