I think it would be a mistake to search for a one size fits all solution, as every family is so different. These are a few general ideas that might help (not listed in order of importance!)
Firstly, you are not responsible for the happiness, well-being and social acceptability of your ex partner.
Secondly though, as a continuing, albeit limited presence in your daughter’s life and therefore your life, it is generally better to have amicable rather than hostile relations.
Thirdly, your own mental health and well-being is an important consideration in your ability to function as a parent.
Fourthly (most importantly), the best interests of your daughter should guide your decisions on contact.
Fifthly, whilst good quality face to face contact is best, indirect contact like cards, gifts, phone calls and video calls can sometimes (though not always) be beneficial for a child’s relationship with her father.
I sense from your posts that we would be in agreement on all of the above points.
Against that backdrop, whether or not you answer a text asking whether you are going on holiday would appear to have no direct impact on the provision of contact for your daughter. The competing issues seem to be the emotional upset to you in having to deal with a seemingly pointless intrusion into your life on the one hand, against the general feeling that amicability is usually preferable to hostility.
Not that this is directly relevant, or that it should dictate your approach as it is hypothetical, but I believe if contact arrangements like yours were to end up in front of the family courts, and the father’s lawyer were to raise that the father would like to know of holidays that his daughter is going on, it is at least possible that the mother’s own lawyer would advise, in the spirit of co-operation, that this is something that would not be unduly onerous to facilitate. It is more than conceivable if a justice or judge was asked to rule on this as a specific issue (which they would be very reluctant to do), that they may in some cases specify that such information be provided, under some broad interpretation of parental responsibility.
I wonder, as others have suggested, whether part of the problem is that unwelcome text messages feel particularly immediate and intrusive by comparison, for instance, to emails. If so, one possibility would be to agree to communicate by email except for the purposes of agreed contact between daughter and father, or in case of emergency. In response to an email about holidays you could then, in your own time, say ‘Yes we’re going to Spain. We’ll be back on 8.8. Let me know if you would like to ring DD to talk about her holiday after we get back’. In response to an email saying ‘how is she getting on?’, you could say, in your own time, ‘Thank you for asking. DD is happy at home and in school. Perhaps you could ring the school office and ask for a copy of her report? Let me know if you would like to ring DD and chat to her about how she is getting on.’ If these emails then prompted satellite requests for more information, you could bin them or respond to them as you see fit.
In relation to the direct contact of twice a year, this is as you say a disappointing level of commitment from Dad. It is, however, considerably better than nothing, particularly if the contact is of good quality. It is also in my view better than the type of father (or mother) who agrees to contact every week and then rarely turns up, leaving their child distraught for the resident parent or cater to pick up the mess. So I don’t think the fact that direct contact is at a disappointing level should dictate your approach to other issues like indirect contact or communication - decide those issues in their own right.
In relation to indirect contact, I would only encourage this where it has potential to strengthen your daughter’s relationship with her father. Firstly, if he is going to let her down, by promising to ring and then not ringing, don’t do it. Secondly, if DD has nothing to talk about, don’t set up a phone call of embarassed silence. An example might be if her father sent her a gift that she liked, she could ring to thank him. Or he could ring after a holiday or joining a new class and talk about that.
If other classmates are making a Father’s Day card, either as a whole class activity or individually, your daughter should feel able to join in with this activity if she wants to, and I think it would be worth an envelope and a second class stamp to send it on. It is also possible that this might just tug at some cord in her father’s mind.
As I find myself starting to write your life for you I revert to what I started with - there is never one magic answer for all families - in fact there are almost always several equally good solutions to one issue in one family. I wish you the strength to find your way forward, and the happiness to enjoy motherhood.