Trying to identify the font used in this woman's tattoo. She wishes to add her son's name Carter, and the date of his birth 04-03-17. Free or paid fonts are both fine, any similar fonts that look as if they would match with the other two used are fine also, thanks for any help!

Those two tattoos are not even similar: you could find a compromise with a balance between the two if you used something like Rhapsody from Ralf Unger available at: https://www.fontshop.com/families/rhapsody

Rhapsodie Swash adds a very nice flourish to the capital letters.