First off, I am not a fan of tattoos, but I think your thought of a mother/daughter sharing link of sorts is quite nice. I'll leave others here to comment more on a tattoo, but I thought I'd offer the idea of something less "branding". I'm referring to maybe a piece of jewelry you can both wear and keep forever? They have lovely rings with messages, and there are also beautiful bracelets, too. Some have special meaningful charms you can buy and add (or easily and painlessly remove) as things change in life. If you buy such a thing that contains a bit of gold or at least silver, the actual item can turn into an investment. A tattoo has no appreciating value in the terms I mention. Also, many bracelets and rings can be custom engraved with words or symbols.

For anyone interested, examples of charms I mention above, can be found at places like Bipolar charms | Etsy I can't fully see the options, because when I do everything switches to what's available only where I am (in Europe). I'm sure the above link has plenty available in the US. Likely many more than available where I am.