Other than her being a bastard child, was any reason given as to why Historia's mother hated her and disowned her?
The reason was that Historia is Rod Reiss's child. Since Historia was his child, she has the ability to obtain the abilities of the Coordinate and use them to the fullest. This was the reason that the Military Police's First Interior Squad had to murder Historia and her mother in order to ensure that power would not fall into the hands of people the central government could not control.
Therefore, Alma hated Historia as Historia's existence would lead to her death.
Historia Reiss - She carried deep resentment towards her daughter, even more so before Kenny slit her throat, as Historia's existence is the reason she had to die.
Another answer is that some women simply cant handle it and reject their first child. Having a baby can be stressful, for the mind and body, in Alma's case unable to cope with the fact that she had gone through something so painful and stress inducing,the fact is she probably only had Historia in the first place in hopes of becoming a Reiss, there for, never seeing her daughter as anything more than a tool to use in the beginning also plays into this. Afterwards she sent away instead of getting what she wanted. Causing her to out right reject the object of which these stress inducing events were caused by, A.K.A Historia.
In short, the woman's a total bitch who shouldn't have had kids in the firstplace, and is blaming a 10yr old so she can feel better about it.