Can someone please help me fix up this sentence (in bold)?

Writing a paper for class. Here is the sentence (the second one is the one need cleaning up here. The first one is just there for your reference:

Ms. Smith in the case In re Smith abandoned her baby by leaving it with a foundling hospital. In a similar way, Ms. Doe in the case before the court abandoned her baby, Jack, by leaving it with WAS, which, like the foundling hospital in [case], would arrange for his further placement.

I think that the second sentence has way too many commas. Basically, I just want to draw the following analogy:
Ms. Smith => Ms. Doe
Smith’s baby => Jack
foundling hospital => WAS (an adoption agency)
Therefore, both mothers abandoned their babies.

Please help. Thanks.