Disclaimer: I am not a groomer, just an owner of two curly dogs that I groom at home most of the time.
I'd actually suggest working on the mats dry or with a detangler spray, rather than soaked. Water can actually tighten mats and make them harder to remove. Cowboy Magic detangler was originally for horses, but I've seen it raved about in dog communities (it's not available where I live, sadly). I have much more success with a metal greyhound-style comb than any brush I've tried; the brushes just don't get down to the skin. My combs have a coarser side with wider teeth and a finer side with very narrow teeth, which is very useful when working out mats.
For very bad mats, you have a couple options. If they're not tight to the skin, you can use a dematting tool. This is essentially a row of blades you hook under the mat and slice up through it, breaking it up so it can be brushed or combed out easier. Mine looks something like this, but they come in a few different styles:
The smooth side of the blades are blunt, which is what faces towards the dog's skin, but you still need to be careful.
If you don't have one, a pair of scissors can do the same thing more slowly. I'd highly recommend a round/blunt-tip scissor for this so you can't stab the dog, especially if you haven't done this before. slide one end of the open scissors through the bottom of the mat and cut upwards, breaking it up so it can be combed out more easily.
There is also a tool called the 'mat zapper', but I've never used it myself so no advice there except that it exists.
If the mat is really close to the skin and you can't get under it, it's probably causing your dog pain and possibly skin damage already, and should just be cut off as close to the skin as possible without risking cutting the dog.
As you might have guessed, all these techniques are time consuming and might honestly be more stressful/painful to the dog than it's worth if they're really heavily matted. Sometimes the best thing you can do is shave the dog down short, if you have electric clippers. Poodle mixes can be notoriously prone to mats, so a shorter coat can make it easier to maintain long-term as well. Heck, I keep my pure poodle short most of the time, because brushing out his entire coat daily is a pain.