You know that's really NOT an issue.....the liquid of the priming solution, really DOES mix fine on it's own. The natural motion of the beer filling the bucket and rising up really is enough motion to integrate it together just fine.
You are mixing a small amount of liguid to a larger volume of liquid, and it's going to distribute itself equally just fine. It's not like we are adding dry sugar to our bottling bucket and mixing that with the beer....the two liquids mix together and the sugar water dillutes just fine.
Inconsistant carbonation,
simple means that they are not ready yet. If you had opened them a week later, or even two, you never would have noticed. Each one is it's own little microcosm, and although generally the should come up at the same time, it's not an automatic switch, and they all pop on.
A tiny difference in temps between bottles in storage can affect the yeasties, speed them up or slow them down. Like if you store them in a closet against a warm wall, the beers closest to the heat source may be a tad warmer than those further way, so thy may carb/condition at slightly different rates. I usually store a batch in 2 seperate locations in my loft 1 case in my bedroom which is a little warmer, and the other in the closet in the lving room, which being in a larger space is a tad cooler, at least according to the thermostat next to that closet. It can be 5-10 degrees warmer in my bedroom. So I usually start with that case at three weeks. Giving the other half a little more time.
Give you bottles a little roll on a table to re-suspend the yeast, and stick them back in the over 70 closet ofr at least another week, or two..and they ALL will be carbed up just fine.
For more info on carbing and conditioning go here;
Of Patience and Bottle Conditioning.
I've never had an issue like that, and I don't stir. I've come to believe that's one of the rationalization new brewers come up with rather than looking at the fact that they simply weren't ready yet.
If you really feel like it will make you feel better. In the future put half in the bucket, then pour half when the level of the racked beer reaches the half way point....
But meh. That's more to make the brewer feel better, than imho it really doing anything.
