Is it legal to bomb ISIL? Really?

One of the things said about the deployment of USA, GB and others' military  hardware in Iraq is that, having been invited to do so by the Iraqi government, it is legal to do so. Presumably we are talking 'legal' according to the United Nations charter. And it is true that the charter grants member states the right to self-defence and to call on help in self-defence. Ostensibly then, yes, it's legal.

But, as I said to someone yesterday, I'm not sure that it is "fully legal". By that is my suspicion that the means and circumstances count against what is actually being proposed. See paragraph 3 of Article 2:

All Members shall settle their international disputes by peaceful means in such a manner that international peace and security, and justice, are not endangered.Charter of the United Nations: Chapter I: Purposes and Principles

Now, I think that this is meant to be consonant with ideas of just war in that just war theory talks about 'jus in bello', that is that the means employed in the circumstances should be likely to resolve the matter with the minimum loss of life, minimum damage etc.

It seems to me that this is an international dispute even though we are talking about non-state actors. I can't see how, once other nations are called in it can fail to be an international dispute: some of the actors are Syrian, and there are Turkish, Saudi, and gulf state interests involved. But the more important thing is not endangering international peace, security and justice. Given the likelihood that going about things in the manner proposed and given the likely next developments (see here) there is very much a danger to security, peace and justice internationally (which also makes it an international concern).

The probability that the repeat of civilian "collateral" deaths and maimings such as we have seen in Afghanistan and previously in Iraq will take place in this campaign. This injustice will further inflame those already frustrated and angry with the West's involvement in the middle east who are likely to seek to carry out violent acts in the wider world and so international security and peace will be further strained and imperilled. In short, the course of action proposed (as it is at this point -I expect it will be approved, sadly) contradicts a fundamental article of the UN, and so cannot be said to be fully legal.

I'm not a lawyer, but I think there is some doubt about the proposal on legal grounds, surely.