I think your “proposed solution” is the only one that makes sense. It’s similar to organizing a party and there are people who are uncomfortable with each other (e.g. ex-partners, friends who argued, etc.): who should I invite? I just invite them all and make it clear who I told to come, they will decide for themselves.
There’s something about airing this on Medium. Although instructive for the general public, it puts your parents-in-law under the spot and biases their decision, which might leave you with the doubt: “would they have made it had I spoken to them directly? Or is it just because they got exposed to such a vast public?”. Maybe we need way more of this bias as a society though.