6-year-old grandchild's tantrums

My daughter's kids, 8 and 6, are with her ex-husband--separated several years ago, divorced in 2019--about 40% of the time, but on a very irregular schedule. He is a paramedic who might have them for 3 days, then not at all for 5 days, then 5 p.m. until 8 a.m. for one day, etc. He tries to be a good dad, but is often too tired to pay enough attention. The 6-year-old boy is a bright, introverted kid who seldom wants to talk about his feelings. He has friends, and gets along well with his big sister for the most part. While his teacher says he's doing fine, he's been having melt-downs at home for the last few months, several times a week or more, and friends have suggested to my daughter that she have him assessed for various syndromes and disorders.

Her ex- is a decent-enough guy who also tends to be negative, sometimes whiny ("I can't buy them new shoes; I'm almost broke."), and has threatened to take her to court to demand 50% custody. He makes considerably more money than she, and seems to spend a lot of it on electronic toys. My daughter is a decent person as well, and talks to him politely, but she's usually tense with anger and frustration after dropping the kids off at their father's. They love both parents, of course, and dislike seeing their father so erratically.

I don't think either one disses the other much in front of their children these days, but I know how good kids are at intuiting their parents' emotions--and overhearing phone conversations, etc. My daughter is a perfectionist who comes to me for both advice and approval. I want to ask whether she keeps track of the tantrums: when they happen, after what event or change, etc. I'd like to bark, "Family therapy, NOW!" but that's easier for me to say than for her to make happen, for various reasons. (I've barked it before.)

My brother is a experienced family social worker, and has talked about our late sister's being the child who acted out our own mother's anger and frustration with our alcoholic father. I think that might be happening here, to some degree. And I wouldn't blame my grandson for being angry on his own account. Obviously it's not my situation to fix, but I wonder whether anyone out there has some insight and advice.

P.S. When my grandson is ready to calm down, he frequently asks his mother to read him Shel Silverstein's poetry; he enjoys the rhythms and the absurd humor. I don't know what this means, but I'm sending more Shel and Kipling and other kids' poets.