Based solely on photos I've seen of the SSD's used in 2013 MBP's, there is a controller chip and 4 NAND chips. The NAND chips are what hold the user data and it's pretty easy to tell them apart from the controller chip because they're the same size with the controller chip being different. The NAND chips may have a label which can serve a heat-dissipation function. If a NAND chip is damaged, then it affects your data. If the controller chip is damaged but not the NAND chips, your data might still be there but as pointed out by another poster, the controller likely holds data on how the user data is organized on the NAND chips. It's very typical that data is interleaved between multiple NAND chips. That is, it will write some data from a file on NAND chip and then more data on another chip. So if one NAND chip is damaged, the data on at least one other NAND chip is pretty useless unless you're talking about some sort of textual data.
I did a quick web search, just looking at the summaries but I did see one data recovery site where they claim to be able to read directly from the NAND chips, bypassing a damaged controller chip. So who knows what's possible? But as other posters have said, I have no doubt that it will be expensive.
I would suggest the following:
1) Other than doing a visual inspection, you should not put the SSD in another computer or remove the label, etc.
2) Talk to Apple, either over the phone or at the Genius Bar. They may or may not have useful information, but it'll be free. Who knows? Maybe there's some defect in some of these SSD's that they're willing to help the user with. Not likely, but who knows? The advantage of going to the Genius Bar is that you can interact in person and you might be able to read something in a person's reaction. I wouldn't put the SSD back in the MBP and if asked, you should be reluctant to have them do the same.
3) Become knowledgeable about SSD's and data recovery and data recovery firms if you decide to pursue data recovery. Do not tell them you have your child's pictures on the SSD and that they are precious to you. You will need to take a step back and decide whether X amount of dollars is better spent on trying to retrieve the data or put in a fund that can be used for college 10-15 years from now.