But in that case, you have made it about the ethics of asking again, not of giving, because it involved the drawing away attention from other causes. Purely the act of giving money to someone so they can have a nice holiday isn't the problem, it is apparently the way they have asked for it.
There could be an argument about this not being "personal gain" because this is about making her children happy, but as we've also mentioned other examples that were about, well, making the beneficiary happy, let's stick to that case.
If your argument is that it is unethical to ask for money because it takes away attention from giving money to more worthy causes, that seems like a harsh rule if you apply it to more general situations. For example, if I am walking along the street with you and I don't have enough coins for a packet of cigarettes, and I am ask you, my friend, for one Euro so I can get me some (let's go with, I am not going to give this back to you because when it comes to little amounts, friends will wave that off), is that unethical because we've walked past a homeless person who is asking for money with a sign?
I suppose my question is whether our giving somebody something always has to be weighed against what and who else we could give this money to. Because if it is, it becomes very hard to live up to this ethical standard. Conversely, the same goes for receiving gifts: there are, after all, people who, on their invitation cards to a birthday party, say "Please no gifts, but instead give a donation to" etc. Now, if I don't do that, but instead allow myself to be given gifts, is that unethical because it serves only my personal gain?