1. The AP takes from few days to several months ...
The average processing time varies over the time.
Usually, you may consider that most of the APs are approved within 2-3 months. However, if you want to be completely safe, you may apply now, as the AP is valid for 1 year since the issue date.
2. The issue of an AP will not intefere the H1B status.
However, once you use the AP , your H1b status will be lost(*) and you will have to get an EAD. (The theory behind that is: when you enter to the US using the AP , your status will be "Paroled ..." , not the H1b )
3. If you want to travel and you don't want to extend your visa, you have the get an AP _AND_ the EAD . Your husband needs the AP only (unless he will work) .
The only thing you may loose is the EAD and AP application fee if you will cancel the travel.
(*) There were some discussions that brought an interpretations of current laws that in fact , the EAD is not mandatory even after you use the AP, as long as your H1b status is ok. However, as far as I know , nobody wanted to be a guiena pig and be the first in trying it.