At which rate does the leader pool rotate

You can check the modifiers by hovering over the red x (or the green checkmark) next to the demand vassalization text. It's a detailed breakdown of which factors speak for and against accepting the demand. If the total number is positive, you'll see a green checkmark and they'll accept the demand, otherwise they won't.

Here are the most important factors:

1. Ethics. Similar ethics provide boosts to this, very important, some ethics like fanatical xenophobe will prevent a peaceful vassalization entirely. You cannot influence this.

2. Empire strength, being stronger, i.e. having the bigger fleet and bigger empire provides significant bonuses

3. Opinion, the biggest factor is opinion there are several ways to increase it: mutual rivals, embassy, treaties (border access, non-aggression, guaranteeing, research agreement), making the empire like you is the most important aspect of peaceful vassalization. Keep in mind, you CANNOT engage into an alliance with them, as an alliance locks you in as equal partners and disables vassalization.

It is generally pretty hard to get a purely peaceful vassalization, especially if your ethics diverge somewhat.

There is a form of military/peaceful vassalization though, that goes beyond forcing an enemy to submit. If in a war, you choose to liberate enemy planets instead of conquering them, this will create a new empire with your government ethics, on top of that, you get a massive +100 opinion for being their liberator. This usually makes peaceful vassalization of the liberated empire very easy.

Ethics divergence is either positive or negative.

If it is positive, it will push your pops' ethics further from your empire's. If it is negative, it will push their ethics toward your empire's. This has been demonstrated in another answer here and the Stellaris wiki.

So, if your empire is xenophobic, and these pops are fanatically xenophobic, then your empire is less xenophobic. Therefore, if you want them to become less xenophobic, you want to push their ethics toward yours. This would require a negative drift.

If you can't get negative, then at least less positive might work. It's not clear to me if the divergence applies equally to each pop, or if it might just be an average of a bell curve.

If you can get some of the pops down to xenophobic, then at some point they might end up less xenophobic than your empire. At this point, you would need a positive drift to continue to reduce their xenophobic tendencies and push them towards xenophilia.