A patch properly makes a good as new repair so there's rarely a reason not to patch, though at some point you have to buy new. Since your cuts are close together you're right to try to get both with a single patch.
The wheel repair can be done as you suggest, but you have to be careful no to damage the good side, or push the blip in too far. Since the wheel also needs aligning, I suggest that you remove the tires and bring one or both in for an alignment and to have the blip fixed. It shouldn't be prohibitive, and I doubt you need new wheels.
BTW- I think your real problem is that you were riding with not enough tire pressure, so I suggest that you're more careful about maintaining correct pressure for conditions in the future to avoid a repeat.
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