When making a peanut butter based sauce, how can I loosen the peanut butter and even out the consistency ? I tried adding a bit of hot water and mixing them, but even after simmering for a while in the pan with frequent stirring I still found clumps of peanut butter.
If you add all the liquids and a big solid lump of peanut butter, you'll have a tough time getting it all smooth, as stirring the (thin) liquid parts won't affect the (solid) peanut butter lumps, and the lumps (once they're small enough) will just swim around your spoon and not break down further.
You need to gradually dilute the peanut butter with the other hot liquids, stirring each time until the mixture is smooth. That way at each stage the liquids won't be vastly thinner than the peanut butter, so stirring will properly mix the two. Once the peanut butter mixture is thinned to the consistency of, say, mayonnaise, you'll be able to add the rest of the liquids.
It's the same principle when making gravy from flour, fat and broth. If you add all the broth at once to the roux, you'll end up with lumpy gravy. But, if you add a bit of broth at a time, stirring until smooth each time, you'll never have lumps.
To fix your problem in hindsight, try running it all through a coarse sieve, or use a potato masher on it.
When making sauces with things like peanut butter, almond butter, tahini, etc., oil is the thing to add to help thin it out. For peanut butter, you could add peanut oil, canola oil, toasted sesame oil, or a light olive oil with a more neutral taste (or perhaps others). I've done this before when making sauces for pasta and it's worked perfectly.
To make sure the consistency is even, you could start with a creamy peanut butter and add oil to it, first mix with a fork and then once it's thinned a bit, you can whisk it to get a more smooth consistency.
As a tip for the future, when trying to thin things out, it's usually a good bet to stick with what the item already has in it. For instance, if you were trying to thin out vegetable broth, there is already a high water content, so water would be the thing to use. With something like peanut butter, it's very oily to begin with, so oil would be the thing to use.
Heat is helpful. I used to make a peanut butter/tabasco/soy sauce satay, and getting the parts to combine cold was practically impossible. Warming the peanut butter first softened it enough that I could beat the other liquids into it with a fork as I added them (and they're both water-based so won't mix very well with the oily peanut butter).
A few seconds in the microwave was all it took.