If you want an I-94 to say its for H1b, then do not reenter on advance parole. Either way it has no effect on any H4's who are in the U.S.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
File an application for extension of stay in H-1B status. Upon its approval you will be automatically reinstated into H-1B status.
If you are paroled into the U.S. then, if you have dependents in the U.S. in H-4 status, they are out of status. I assume that they are automatically reinstated into H-4 status if you are reinstated to H-1B status, but the law is not clear, and the most prudent course would be for them to apply for an extension of stay with you.
An experienced immigration attorney can guide you on review of your H-1B documents.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.