What do you do with your husband's mother who avoids you and ignores you in public for fear of her husband's jealousy?

The wife's mother is a mahram to her daughter's husband, so there is no harm in him speaking with her or being in khalwa (private seclusion) with her. As for the wife's father's jealousy regarding his daughter's husband speaking with the wife's mother, it is a type of excessive jealousy that is not appropriate. If his jealousy is not based on suspicion, then he should be informed of the error of his actions. If he does not desist, then one should avoid speaking with her in his presence to avoid problems.