I don't think that Eilis's mother would ever have moved to the US, and I don't think that, if she went to visit, her liking Tony and his family would be at all a foregone conclusion. She is someone utterly schooled in the snobberies and social gradations of smalltown Irish life of the 1950s, and, however kindhearted, would have seen Tony, at least initially, as a disappointingly blue-collar foreigner from a poor non-English speaking family who eat 'funny food' -- and, of course, the one who 'forced' her daughter into throwing away all the opportunities that could have been hers at home. Plus she would have been utterly hurt and humiliated by the revelation of Eilis's secret marriage, and the flood of malicious gossip it would have caused after Eilis left again so suddenly. I think it would have taken her a lot of time to effort to 'forgive' Tony for that.
I also think Eilis would not have invited her to come and visit until she and Tony were in a much more obviously prosperous situation. Otherwise the comparison with the life she could have had in Ireland with Jim and an assured position in the social and economic life of their town would be too obvious and painful to her mother, and their would have been a lot of 'accidental' comments about how lovely Jim's wife is, how well-respected Jim is, and how rich they are etc.
Her mother isn't an entirely benign character either. Colm Toibin is very good on open-ended gestures from mother-figures that are capable of several interpretations, but are difficult to call someone on. Mrs Lacey doesn't accept the wedding invitation for a week after Eilis should have returned to the US by accident, or just out of an understandable desire to have her daughter with her for longer -- she doesn't say 'Please stay on another week, so we can go together'. She accepts on Eilis's behalf and pressures her subtly into staying longer than planned, and, by never asking anything about her life in Brooklyn, refuses to acknowledge Eilis has changed, or has a life elsewhere.
And going upstairs to bed just after Eilis has confessed that she's married, and refusing to have the frank conversation that E wants, or spend a last few hours together, or to say goodbye to her in the morning, is also a powerfully passive-aggressive way of punishing her daughter.