In 'An Inspector Calls', how far does Priestley present Mrs Birling as an unlikeable character?

Priestly's opening stage directions already condemn Mrs Birling as "a rather cold woman". At the same time, however, Priestly continually describes her as "his [Mr Birling's] wife" in these stage directions, denying her a name and therefore identity beyond the objectified wifely position - a relegation more sympathetic from the reader's perspective than her initial description. However this denial of identity by Priestly suggests his dislike of the character and perhaps an intention to present Mrs Birling as a generalized wifely object in order to suggest her emotionless objective function in the family 'machine' - a metaphorical presentation well-fitting the industrial context of the play.
When the action of the play begins, Mrs Birling starts out as "smiling" and "reproachful", however it is clear that her tentativeness is only a guise through which she exerts control over others, telling Arthur not to "say such things", speaking for ("Of course she does") and lecturing ("Now, Sheila...") her daughter. Her function seems to be maintaining the boundaries of family function, but this creates instant dislike in the reader/audience as she appears to stamp down other characters' individuality to maintain a false representation of family. Her control is only limited by Mr Birling, who even she cannot stop on his long after-dinner speech, but she still tries to maintain the upper hand by standing first immediately afterwards, followed by the others at the table.
Mrs Birling is unlikeable because she is controlling, and delays the reader/audience from being able to engage with the true nature of many of the characters as they are corralled and controlled by her part in the delicate game of the family performance. Priestly's structuring of the play to leave Mrs Birling out of much of the initial reveal brought on by the Inspector allows the reader/audience the immense pleasure of watching Mrs Birling tear herself down in her own attempts to maintain normalcy and dismiss the suicide issue raised as one concerning "Girls of that class". Her very controlling language is torn down by none other than her own daughter, Sheila, who laughs uncontrollably at Mrs Birling attempting to use "impertinent" to condemn the Inspector's behaviour. With the contrast of the enlightened Inspector, the backwards conformism of Mrs Birling's ways are truly revealed, as too is Priestly's not just unlikeable, but detestable presentation of her.