Chiming in a little late here but wanted to give you my input...
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My toddler doesn't get to watch much TV, so I use it judiciously. When my infant's nap time rolls around, I turn on a show that will hold my toddler's attention for 20 minutes. Then I sit with him on the couch and nurse my infant until she's zonked out. At that point, I'm able to sneak off and transfer her into a cradle swing (where the motion tends to keep her asleep without the need for too much soothing from me). By the time I'm done with that, the toddler's show is just ending and I can whisk him someplace as far from the napping baby as possible...
