The correct usage of commas would be as follows:
Infants should stay at home or, if their parents both work, go to daycare.
These are bracketing commas.
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Note how your original comma does not fit into any of these categories. If you want to use a comma before "or", both that before and after the "or" should be able to be stand alone as complete sentences:
Infants should stay at home, or they should go to daycare, if their parents both work.
Here the second bracketing comma is replaced by a full stop. This is fine.
Note that bracketing commas can be optional if the sentence is clear without them. Therefore, this is also correct:
Infants should stay at home, or they should go to daycare if their parents both work.