“If Umm Salama (RA) was among Ahlul-Bayt, why didn’t the Prophet answer her positively?”
And neither did the Prophet (saw) answered her in negative.
“Why didn’t he enter her into the cloak?”
If he had, then you would have said that she is acceptable but not the rest of the wives.
If the only criteria to be form Ahlul Bayt is to be under the Cloak of the Prophet (saw); How come you take rest of your nine imams (raa) from Hazrat Zainul Abidin to the Last one (may Allah be pleased with them all) from Ahlul Bayt?
They were not under the cloak yet you consider them to be from Ahlul Bayt.
“Why did the Prophet tell her that she remains in her own position?”
In your bias, you see that the Prophet (saw) has excluded her ( Hazrat Umm Salama) (ra) from the Ahlul-Bayt.
In my bias, I see that the Prophet (saw) is reassuring her (Hazrat Umm Salama (ra)) of her status as the member of Ahlul-Bayt (may Allah (swt) be pleased with them all) by saying; “You remain in your position and you are toward a good ending”.