I took "Once burned" to be the equivalent of " once bitten, twice shy" and thought that once underlying meaning could be, apart from the obvious one that marriage to alma hadn't made him happy, that he was still making tho child-support payments and didn't need any more finanancial responsibilities.
I'm sure Alma would like him to marry again, since he'd be off her conscience - she seems to feel a sense of responsibility for him - and woul if re-married look more like what her conventional mind told her a man should be - married, settled, etc. I also wonder if, given the way Ennis lives, she feels that she might to some degree be blamed for that - the implication being that supporting the girls has impoverished him.
Still, as she saw the reunion kiss, it seems a particularly crass thing to say unles she's trying to stir up some sort of reaction. Maybe she wants to know, once and for all, if he really is gay, in which case she's be justified in having left him. Or maybe she's been bottling up her resentment and frustration with Ennis and it breaks out here, much as Ennis's bottled-up passion for Jack breaks out in the reunion kiss.