I've always heard of the 28-week rule, which I thought was supposed to protect pregnant females from being kicked out of the barracks before that time.
How far along is she at this point, and has she been given a pregnancy counseling outlining housing options? I know the on-post housing list at Bliss is insane amounts of long, but it's a viable alternative to receiving BAH and an avenue she might want to explore. She can be placed on the waiting list once the pregnancy is confirmed, but can not actually move into family housing until the birth of the child. You already referenced AR 420-1
which says: (5) Pregnant military personnel, otherwise without Family members, may be placed on the waiting list when pregnancy is confirmed by medical authority.
(5) Pregnant military personnel (with no other Family members) will not be assigned to Family housing until the birth of the child.
As for receiving BAH, it's harder to find in the regulation, but from what I can gather it can vary by post policy and the discretion of the commander. The above referenced regulation also says: (2) Garrison commanders may authorize single Soldiers in the grade of sergeant (E5) and below to reside off post under the following conditions:
(a) When adequate housing is not available and military necessity is not a factor.
(b) When the Soldier is pregnant.
(c) When the Soldier has purchased a home near the installation prior to notification of assignment to that installation.
I found a few post policy letters outlining the 28-week rule, but still can't find it in any Army-wide regulation. Fort Irwin Fort Riley
Try as I might though, I can't find one for Fort Bliss. Honestly I think it's a little ridiculous myself, and I definitely understand your/her concerns. It definitely sounds like she's getting set up for failure, because you're right, what if she has the baby early, THEN has to fight for BAH and then gets the joys of trying to move into a house or apartment with a newborn? Truthfully it seems like it's really up to the command how it gets handled, and I don't know what sort of advice to offer in that situation if the command plans on screwing her around.
If I find anything else out, I'll let you know.