I would say the UK, France and USA could dictate whatever terms they saw fit. Looking at it from the British vantage point of 1918 the world is quickly moving to what they termed Bolshevism, Marxist revolution was brewing everywhere, and even the French where looked upon as "revolutionary" to the conservatives in Britain, after all they cut the head off a King and gave them Bonaparte. It would have been justice enough to force both the Kaiser and the Crown Prince to abdicate while letting then lawful succession set the grandson on the throne while a new more potent Diet is formed under the watchful eye of the victors, more easily nudged to something like familiar Parliament. And the British keep the orderly monarchy in place versus an uncertain revolutionary future. It gives the Army and conservatives a lot of room to sell peace at the price of an unpopular Wilhelm, reparations are just money, the reforming liberals and SDP gets more power without the Communists, a reduced navy doesn't concern the Generals much and a smaller Army with less offensive bite but enough to deter the USSR gives the UK far more than it got from Versailles. Germany easily could have gone Bolshevik and into the Soviet orbit, that could not have been beyond everyone at the wrangling over the Treaty, and to the British the Treaty should have been obviously an unraveling of the Europe they understood as a place to dabble in but never get too deeply entangled with.
In this case, it doesn't matter, as they were pretty thoroughly overtaken by events before there even was a Treaty of Versailles ready. And demanding a restoration of the monarchy as part of the terms would have been utterly despised by Wilson, who supported any form of self-determination that chose the form of government he thought was best. Honestly, it's hard to see the French going along with it either; they wouldn't want any provisions that could ruin the rest of the treaty, and they obviously didn't have a fervor for monarchy either (and given how powerless the monarchy had become by this point in British history, it can't be said that they cared about monarchs other than their own as much), so getting them to possibly be forced to help restore a monarchy after a ceasefire had been called would be very unpopular with the troops. Lastly, it's not a credible anti-Bolshevik measure. Yeah, the death of the French king led to Bonaparte...which is to say, that deep-seated dissatisfaction with the King led to Bonaparte. More immediately, they also saw a monarch get toppled and then a communist uprising; you'd have to be pretty dim to assume that restoring the Tsar between February and October 1917 would have made the difference. It wouldn't provide any additional stability, but merely discredit the Prussian aristocracy and the SPD government that would be forced to sign this. Who would fill that void of basic legitimacy? Someone sane like Zentrum, or the KPD? Maybe someone even worse?
More than that, you can force a lot of things onto a defeated enemy in a situation like this, but you can't ask that the guys you're negotiating with sign away their domestic political power. Even if they were actually your toadies, they still wouldn't have the power to do that. That requires additional force, which in this context would mean resuming hostilities after an armistice had been declared. Nobody in Britain or France would have supported that.
As for sitting out of the OTL war, you should remember that in a France-Russia vs. Germany-Austria war, they fully expected the former to win, and what's more, it was clear from French naval deployments that they expected British support. To do anything but declare war on Germany would have been seen as a betrayal, and if they had sat out and the Entente won anyways, then they'd be faced with a true disaster, as the French would dominate Europe and be in a position to punish the British for reneging on perceived commitments. They'd be undamaged, but also deprived of influence on the continent with anyone of consequence, and in no position to moderate Franco-Russian dismemberment of Germany. In hindsight, this overestimates Russian strength, yes, but everyone did at the time, from Berlin to Paris to London. They'd taken pains to avoid seeming too firmly committed to one side or the other, but the French effectively forced their hand, and the Germans gave them too good a pretext not to honor their "commitments".