No, you, nor anyone else can 'sponsor' someone's tourist visa ... they have to be self-sufficient.
I can tell you that mentioning your pregnant wife, if not done correctly, can hurt their application.
And, yes, you are correct, an expired visa stamp is not important ... as long as the I-94 is current.
But, again you can not 'sponsor' someone for a tourist visa.
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Your parents have to each qualify for obtaining a B1/B2 visa on their own. They have to show "substantial ties" (connections) to the country of nationality and Intent to return after a temporary visit to the US.
Wanting to visit their daughter who just gave birth is OK, but they cannot state wanting to "babysit" the child or otherwise help to care for and raise the child. US governmental agencies do not like that, as it is considered working without authorization and competing with US workers.
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I agree with my colleagues. You cannot sponsor your parents.
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