There's also the little fact that ITTL, Japan is in a stronger position, in other words, can retaliate with chemical weapons on Australia and possibly NZ if the USA manage to nuke Japan. Worse, if Germany (or France) is nuked, Britain automatically gets gassed (as both French and Germans either have chemical weapons or can produce them easily). Even Spain and Italy, if nuked, might be able to sneak submarines with chemical bombs (on suicide attacks) into British ports in answer. Not likely, but the Allies can't be sure it won't happen.
Oh, and last but not least, in '44-45, the ACP will have secure access to uranium (either through Imperial Russia or French colonies or both). It's likely that the Amerika Bomber and Nakajima G10N Fujaku projects will be more advanced than IOTL, with both the ACP and CPS in stronger position (and possibly actually cooperating together). So, if the USA used nukes on their enemies, said enemies might not only retaliate on Britain and her dominions, but also on the USA themselves (with intercontinental bombers and/or subs carrying radiological, chemical and bioweapons).
Nukes are only useful if you're in a really really desperate position (like : your enemy is invading, you have no chance of stopping them, and occupation is worse than death, for example the Draka), OR if you're in a position of total dominance (ie. you're 100% sure that the enemy can't launch WMDs at you or your close allies), but where conventional war would be too costly. Or if your enemy has started using WMDs first. In any other scenario, using nukes is absolute stupidity.
Dewey is right. Nukes are a bad idea in this scenario, tactically speaking (not going into the ethical debate, which is another problem).