Honestly, i think most of the comments are missing the point, OP *seems* to be asking if we think it's an issue with his tyres or the car itself.
OPs Issues:
1. They're struggling for grip in the wet.
2. They have miss-matching less known tyres on the front.
My comments on these issues;
1. Unless the alignment is out (which i'd assume they'd have had done after the pothole), it's most likely down to the tyres.
2. The front is the important axle, most of the load goes through the front tyres, braking, steering, accelerating, almost all of that is through the fronts, you want the better tyres at the front.
Continuing on that;
The 16" wheels OP has already, are a good compromise between good handling and good ride quality/comfort, going down to a 15" with 185 width tyres is less rubber contact, less grip, that's not going to help OPs issue.
The Dunlops (i'm assuming SP Sport Maxx) are among the better ones in terms of grip and handling, so there's no need to change them really.
Ideally, you want the same tyres on all 4 wheels, failing that, you want a good matching pair on the front.
So that leaves two main options;
Swap the fronts and rears over, so the grippier dunlops are on the front, where they matter.
Replace the existing fronts with new dunlops, so OP has matching tyres on all corners. OP can sell on the part-worn ones to make a little money back.
Final consideration;
Roads *can* *sometimes* be quite slippery when first wet after a long dry spell. I don't know what the weather's been like leading up to OPs incident, but that could play a role.
New tyres don't necessarily grip well "straight out of the box", the tyre may be coated in something to preserve it in storage (like some brake discs are) or just to look pretty, the very first time I had my front tyres changed, i almost went into the middle of a roundabout from spinning the wheels up trying to pull away quickly and understeering badly.