I have had the same sort of experience, noting a very strong internal reaction (not really related to the present moment, in terms of not REALLY related to the actual stimulus, though of course triggered by the present moment) and a clear impulse to control, when my daughter (my first child) was very young. Extrapolating mentally, I could tell that it could escalate tremendously and that if it did, if she didn't give in or give up, I would be really stuck (if I followed that path.) It was very strange but I recognized it as what I absorbed from my father. (I don't know his experience specifically, but that was the message I internalized: the importance of winning, of maintaining control when "challenged," at any cost.) It was bizarre to feel that, and to see it critically, but still feel it.
I agree that "Parenting From the Inside Out" is a good resource. Much info from Daniel Siegel is similarly valuable. A practice of mindful presence is probably the best discipline for developing a compassionate, non-judgmental Observing presence that will help you observe your reactivity to the point that you can see it instead of being it. Connecting to your own validity, even when your behavior or impulses are not in line with your values & ideals, seems to go further toward being able to respond compassionately to a child & connect consistently to his validity in the moment (despite the behavior) than any attempt to do so "on principle." (For me, "connecting to the child's validity" is just a way of expressing an ability to see behaviors in terms of the underlying needs they express or suggest, to see behaviors as strategies to get needs met or as expressions of good things.) This is harder when a behavior is triggering, for whatever reason.
In my experience, connecting this way comes more naturally when it is an outgrowth of how I see and treat myself, rather when it's just something I try to give my child because I believe in it. I think that's because doing right "on principle" breaks down at some point if you are stuffing your own feelings & reactions in order to pull it off. But if you are giving yourself and your reactions compassionate presence and acknowledgment, then you are validating yourself and less likely to reach the breaking point and "snap," and less likely to struggle to parent by your ideals (it will come more naturally, if you are parenting yourself the same way rather than judging yourself harshly.)
There are lots of avenues for cultivating this...."mindfulness" or mindful presence, Vipassana meditation, Focusing, the non-judgmental Observer of Non-Violent Communication, Hakomi therapy, and other mindfulness centered therapies.
Staying present in the moment, focused on acceptance (rather than judgment and resulting resistance), is a useful practice.
Recognizing that any other-focused or outward-directed emotion or reaction indicates the same sort of feeling directed at yourself also is helpful. I don't always find this is enough for me in the moment (sometimes it is), but even if only my awareness is engaged (but isn't enough to stop my reactivity), it makes reconnection & self-knowledge/realization that much quicker, and it makes me MUCH more likely to be able to take responsibility for myself and my reactions out of really being connected to that responsibility.
But even when your annoyance or upset is not enough to generate actions, just recognizing other-focused feelings such as irritation, blame, criticism, anger as they arise in yourself is useful as a reminder to notice there is something going on, something painful & threatening that you are escaping by turning those feelings outward. Then it's a matter of looking within for the unconscious or unquestioned thoughts & beliefs ("a good mother would know how to fix....", etc.) that trigger intolerable feelings in us when we encounter self-doubt, etc. Locating blame with someone else is a way of escaping something painful or intolerable within, so if we can observe our anger & annoyance as a signal of something unconscious within, we can begin a process of "deactivating our buttons." I also notice, in myself (and in my kids), that the impulse to control/overpower/intimidate/threaten is related to fearfulness & powerlessness, a victim position, a feeling of "if I don't take this into my own hands/force this outcome, I won't/can't have what I need." Sometimes just noticing the impulse itself can help tune me in to (or help me to know there's something to tune into!) the fear that I have, or the assumption I'm accepting (that X is necessary for things to be okay.) This can extend to soooo many things where young toddlers are concerned, and connecting to it in yourself can help with attuning to your child, rather than reacting because of these fears and feelings.
But overall (and I think this is what Siegel's book is advocating), when we can observe whatever arises in us with compassion, understanding & non-judgmental acceptance, then we are "re-parenting" ourselves in a way that heals old wounds. (This happens via literal re-wiring of our brains, making better more optimal neural connections.) We are providing for ourselves unconditional positive regard (rather than the conditional positive regard the majority of us received when parents and others used approval to influence & control our behavior, usually starting in toddlerhood.) And this makes it increasingly possible for us to reliably provide unconditional positive regard to our children (not just because we want to or are trying to, but as an extension or outgrowth of an inner shift that makes it more & more natural to connect to the validity of another, even in conflict, because we're connected to our own validity.)
I think the crux of it is that the more compassionately you can see yourself, the less personally you tend to take things (or the less triggered you are), because you're not as needy or as threatened (not as defended.) So you can more easily see things as they are.
I haven't exactly tried to express these things before, so I'm sorry it's pretty cumbersome.