If Britain had indeed granted the Dominions a greater say in the running of the first world war and taken more care with the soldiers - would they be able to keep goodwill after the peace was signed ?
Also if britain stayed out of the first world war altogether could it possibly federalise or unify with any of its colonies in that time period ?
If you avoid the UK in WW1, it looks much different than OTL. The butterflies are massive and numerous. Basically, you get a CP win with a German MiddleEurope trade zone. And without the shock of WW1 for the UK, why would the UK want to redo a political deal less than a decade old? (Dominion Status 1910)
Now they had a War Cabinet, which was a pretty big step for the English mindset. Exactly what are you proposing as the POD? I don't see how in the mist of a major war, the UK does its most significant structural reform since Cromwell took power. Stranger things have happened, but it looks likely to cause issues. It is roughly like FDR asking for a DoW and a Constitutional convention on December 8th. And I don't see moving up the bringing of Colonials into the war cabinet earlier is a big help.
And to have the settler colonies vote on joining requires reforms in the original dominion process. And what you are wanting seems to be the reverse of what was happening. So you are asking for a 180 political swing. BTW, are you aware South Africa considers its independence year as 1910? The horse is already out of the barn, as they say.
And even if you do some POD well prewar and decide to ignore the butterflies, I don't think the English power structure will like the change. So handwavium, lets assume some type of integrated structure exists towards wars. Lets look at how it happens, and some things the UK will not like.
1) Germany declares martial law, first day of mobilization. IOTL, the PM can move decisively after he gets cabinet approval on a secret, really unofficial treaty. ITTL, he now has to consult Canada, SA, Aussies, and NZ. So now before he can send BEF, you need 5 votes or 5 PM agreeing. It will cause a delay of several days to weeks as the PM explains he negotiate a treaty in secret. The first weeks of the war did not go well in France IOTL, and worse in ITTL. The process will be blamed.
And how did you expect the process to actually work? Details will matter a lot. I think you have had another thread on what it takes to federalize the British Empire (now renamed Indian Empire). There are a host of issues related to having a new Imperial parliament that is superior to the House of Commons. And if you have the House of Commons/Lords become the new imperial parliament, there is a host of issues, just different forms.
2) South Africa will be enthusiastic to join war. But they will bring up other issues the English parliament does not like such as they want control of Botswana. England will just need to cave on it. It is not really a big issue, but it will be an emotional issue for the English. It is the son telling the father how to run the household. Also issues with Rhodesia, but these can be fudged for now.
3) You lack forces to take Tsingtao unless you keep ANZAC home, the main overseas German naval base. Aussies will never accept island going to Japan. The solution is simple, the ANZAC forces used in Gallipoli will be used to take Tsingtao in 1915. It will be a slow but successful attack. Now think about someone like Churchill being told that he can't do Gallipolli because the Aussies overruled him. BTW, I am assuming Aussies and NZ can agree to a Pacific strategy. And even though in the long run, the British Empire will be much better off for not giving Japan an opening into China, the English will resent this decision.
4) Canada is fairly easy early on, but I think they will be more concerned with the American objections to the blockade. It is not a big issue that can't be fixed, it is just the attitude change for a PM or Sea Lord to have colonials tell them they can't do X or Y is a big one.
5) It will not be called Affirmative action, but I bet there will be huge fights over the number of flag officers in the Army and Navy. The white settlers colonies are over 1/3 of population. Did they have anywhere near 1/3 of 3 star and 4 star ranks.
6) When we get to end, we have more parties at ToV. It makes for even harder negotiations.