Are you familiar with any systems of household Dharma practice that are specifically focused on interactions with your spouse and children? Not just standard advice such as practicing virtue; I'm more thinking of stuff like exercising metta and empathy intermingled with some form of insight practice (e.g. stretching your sense of identity to include the other person, thus indirectly relativizing the illusion of separate self). So, not pure insight (such as just noting the sensations during the interaction), but insight infused with psychological qualities which are beneficial for your family (if possible).

Some related examples that I am aware of: John Welwood's practices, Vajra Romance (from Aro gTér)...

Nice one! Being a family dad, with a partner and two kids Im joining this thread in hope we get some good stuff out of it. 

Will try and chime in once I get more time. 

You can look up Buddhist Geeks/Vince Horn since based on what I have seen they are integrating social aspects to meditation.  They have this thing called Social Meditation wherein  you involve other people into your practice. It has many applications like social noting wherein noting but just between two people etc.
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You can check this out: https://twitter.com/VinceFHorn/status/1410952531614867458 

edit: although on reflection its not family specific but more on social relations in general 

Disclaimer first: I don't have family

For communication (in general, but also with partners, where emotions jump; not tested with kids) I find the Non-Violent Communication framework really excellent; it relies heavily on mindfulness (though they don't use that word, presumably because it predates the mindfulness boom, and is not explicitly rooted in Buddhism). This is a workshop recording (watch it with your partner together, tested!): https://www.youtube.com/watch?v=l7TONauJGfc — it is quite fun in a way, and very down-to-earth yet profound. Marshall Rosenberg also gives examples with kids. As for books, Living Nonviolent Communication was the one I enjoyed the most. The basic skills are distinguishing thoughts from feelings, observations from judgements, learning to hear what other need (as opposed to what they say), and how to express one's needs in a way to be better understood; and so on.

I read and have heard praise on Eline Snel's books with easy mindfulness exercises for kids and parents: Sitting Still Like a Frog (for 5-12 years) and Breathe Through This (for 12-18 years). My son in law (5 years back then) learnt how to fall asleep by putting thoughts into various boxes as they were coming (especially, as he told me, chocolate-thoughts into sealed boxes ;) ).

There is also Jon & Myla Kabat-Zinn: Everyday Blessings: The Inner Work of Mindful Parenting, which I did not read (yet) but seems to a be a classic in this direction (Kabat-Zinn is the guy who made mindfulness mainstream through MBSR, just in case).

Not many answers in this thread... I must wonder whether this is a deeper reflection of the fact that our "subculture" is, in some ways, an union of Theravadin monastic teachings and western individualistic mentality

I find family life with young kids to be full of opportunities for uncovering and working with my reactivity patterns! I've also learned a lot about how my own parents treated me, because that's the default mode for how you relate to your kids (and feel about yourself).

I think that the book "The Spectrum of Ecstacy" has heaps of workable material in there that is applicable to family life and social life. 

I find that that the general workable parts of the path are found in the Sila teachings. Trying to cultivate maximum generosity, loving-kindness, and wisdom is the way to go -- keeping mindfulness in daily life of how we act, trying to always angle towards skilful means. They all go hand-in-hand. 

Hi Griffin, many/most of what you mention in your OP happens naturally when you have a family. I already had some pyschology background (as a client) when my kid was born, so when old stuff came to the foreground I had some psychological tools to work with. I've learned a lot, still much much to learn. Working on reactivity patterns is a life endeavour I guess.

I would add to what you posted: close everyday interaction with your elder parents, those that are too old to be on their own.  Unresolved issues + health issues + mirror dependency (your parents become your kids) + death, a great combo for dharma practice, isn't it?