marthak:
First H1 holder is the primary applicant. Since you have not used your EAD, you are elligible for H1 extension. You can travel using H1 or AP which ever is convienient to you.
Since your spouse has used EAD, she has accepted AOS. H4 is no more valid. Since H4 is no more valid there is no question of applying H4 ext too. For travel purpose she has to use AP.
If you have a child dependent..., his/her H4 is still valid as long as you maintain your H1 status.
You being the primary applicant, if you use EAD, then all your dependents too would be in AOS, for travel purpose every one of you should use AP.
tiredwarrior:
For H1 extension only your sponsoring employing company has to apply I-129. Filing fee for I-129 is just $130 + mailing charges. Any person who is performing HR duties can fill in the form and attach the required documents. First time filers may have numerous question but not at the time of applying extension.
Unless your company is cheating you, you do not need to pay even single penny for H1. Also remember, companies charging the employee for H1 is illegal, ofcourse this is very common from consulting companies.