Look, I know I shouldn't, but....
The question the OP raised is context specific, it is a decision that involves (at least) four human beings. To say whether he is being unreasonable is not about whether he 'as a father' can do something or even, as some here have made it, whether he has a 'right' to do something, it's about whether given all that can be understood about the situation it is on balance fair, justified, reasonable even to prioritise who he does by going (I have rights to do all sorts of things, doesn't make it right to do them). That situation is not about what he 'as a father' does with kids, or even what is 'best' for his DD, it's abouit four people struggling to support each other in a difficult and complex world.
Those (toniguy, exoticfruits, others) who wish to make this a gendergeddon exercise (a man being nice, not this man, let's flip the roles etc.) concern me because I find that father's rights rhetoric both hateful and unhelpful. Because it is undoubtedly true that men as well as women suffer from the expectation that women do childcare. It's true for men institutionally pushed away from doing what they'd wish, pushed out by their partners, or for those who do shorter or longer stints as SAHPs and find themselves in a strange world where the highest praise is to be 'as good as a mother'. But its more true for women, not just SAHMS, or even individual women with kids, but even women who have no kids at all. And there is something very disturbing about missing that when pouncing over every case where a man as man seems to be being picked on: here it meant missing key details of the situation because of how the OP phrased his point, generally it means dismissing those details because the point is the man not the woman.
Because somewhere in my mind is a dream of a world in which these assumptions are less binding, and as I've parented I've seen how it can be effected, by those like me with the privilege of being male being aware of it, not screaming at every perceived gendered injustice to those who suffer most, accommodating, building trust and support networks from other parents (well, let's be honest, mothers) we know, watching their trust grow and ever so slowly moving forward over a thousand softplay sessions, SureStart groups park benches and, eventually, coffees and cake at home. And all that, and the friendships and support that can be built for the next man to enter a baby group looking to find some support as a parent, or to move in next door with two kids to look after, are profoundly threatened by every loon, in RL or Mumsnet or the internet generally, who responds as if the key thing that must be understood by mothers is that men have it hard too, when actually we have it much, much easier.
Self-hater with agenda sounding off and out.