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I am sorry to hear about this situation. Understand first of all that someone who receives a B2 visa does not have a guaranteed right to enter - this is still at the discretion of the authorities at the entry point (ICE/CBP), wh may deny entry, or, may limit entry for less than what the visa normally allows.
It sounds like what ICE/CBP believes is that your mother is using the B2 visa to "reside" in the US. Someone who is on a B2 visa is expected to spend as much time abroad as they did in USA before reentering again on the B2 visa (this is subjective). Because your mother has been spending less time abroad and more time inside USA (not counting the 9 months), the authorities believe that she is abusing her visa by essentially "living" in USA. This is likely why she is being denied entry.
She wants to explain to the authorities that she has no intention to stay here long, and, will ensure to spend at least 6 months abroad before coming back. She also has to be able to show a fixed residence abroad. If she has employment abroad as well, that helps - whatever shows that she lives her life abroad and is coming to USA to visit, and not the other way around.
I am afraid that at this time, it is really up to the authorities to decide whether or not to let her in.
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