KubaFYI, in light of the update you made to your question, I am submitting a second answer for your consideration.
The title of the question is "How can I make my family understand my CO2-emissions-related hesitation to fly in order to spend time with them?" In the update you say that "This question was meant to be ... more about how to negotiate a lifestyle choice where some sacrifices need to be made in order to form a sustainable society."
It would seem that the two highlighted sections are at odds with each other.
Negotiation is a dialogue between parties to address a point of conflict and obtain (usually via compromise) a beneficial outcome for one or more of the parties. If you have adopted a stance that is non-negotiable, then this has nothing to do with negotiation and all about imposing your choice on others.
I do note, however, that you visit at Easter and Christmas... so it could be that you feel you have already made concessions to your "no fly" rule and you may feel it is unreasonable of your family to expect any more?
In any case, think if it from your family's point-of-view: "We love our son. We gave birth to him, raised him, provided for him, educated him, and now he's run off to a foreign land and we barely get to see him any more. He doesn't even think it's worth using a little bit of fuel to come visit us. Family visit each other — that's what families do. If they don't visit then they're nothing more than strangers. It's like he's deliberately trying to avoid us. What's wrong with him?"
Of course it would be presumptuous of me to say I know exactly what your family is thinking — the above is presented just to get you thinking about what might be going through their minds.
Further, your dad might have thought "Well, if our son doesn't think it's worth visiting us at home like he normally does, maybe if we spice it up by going somewhere different he will be more likely to come?" Maybe your father loves you so much that he is willing to spend a whole lot of money to lure you to that remote location just so that he/they can spend a few more days with you?
If we look at it from that perspective, the issue seems to have nothing at all to do with emissions and sustainability and everything to do with observing cultural norms and maintaining the strength of the family unit.
I faced the same issue when I moved several hundred kilometres away from home for education and work reasons a few decades ago, and so have millions (perhaps billions) of other people over the ages. It's nothing new.
Parents can understand children not visiting if it is simply not possible for them to do so (e.g. they are working, don't have enough money, car has broken down, have to look after livestock, medical issues, etc.) but that is not the case here. In this case you are choosing not to visit. Your reasons are irrelevant. Nothing is preventing you from visiting — you are making a choice not to visit.
Your parents don't (perhaps can't) understand or accept that choice because "maintaining the strength of the family unit" is supremely important to them. Bonds between family members are emotional — they are not logical. Logical arguments (emissions) do not apply to emotional bonds (kinship) — such arguments are like water off a duck's back. Love trumps all.
If we distill your situation to its very essence I think it ends up looking something like this:
- You do not value family bonds as much as other members of your family do
- For 'reasons' you choose not to visit them as frequently as you are able to
- They feel that your choices are threatening the strength of the family unit
- Frustration is felt by both sides because 'the other party' just doesn't get it
- Communication will improve if you both speak the same 'language'
- This is an emotional issue, not a logical one
- Emotional intelligence, language and arguments will be needed to resolve the issue
...and at that point we are well outside of the scope of the Sustainable Living.SE.
If you are resolved to pursuing this path (despite there being no mathematically-supported need to do so), then the Interpersonal Skills.SE is perhaps a better forum to consult for advice on how to tactfully talk to your family and get them to accept the fact that you don't care about them as much as they care about you... because that's what it boils down to.
Note (for anyone feeling triggered at this point): None of the above should be taken as a personal attack. It is absolutely normal for there to be children who don't value family as much as their siblings or parents. (I, in fact, am one of them.) History is littered with individuals that reject social norms and/or close family ties. History is also littered with individuals that take ideological stands on issues — often at great personal cost. All that I am trying to do is to make the real issue as clear as possible to assist the OP in moving forward.
tl;dr: It's not about the CO2 — it's all about the feels.