@fitzyafcb if I've got that right, on a two lane piece of road you had car car bike all next to each other with your car the one in the middle? That was definitely your problem, no way it was a safe manoeuvre and no surprise people got irate.
The cyclist wobble was probably part of the shoulder check. It's not unusual for you to unwittingly move the bike when you look around, partly because if you're not thinking about it you move your shoulders which effects the handlebars, partly because you tend to go where you are looking. Again if that caused a problem, then it was because there wasn't room to do what you were trying to do. Basically if you wouldn't put three cars side by side on that bit of road, don't be the one that puts three of anything else there.
Filtering through traffic is a bit of a special case, if the traffic is moving slow enough that splitting lanes is safe then it doesn't really count the same way as vehicles moving in free flowing situations. I'm presuming the OP was with free flowing traffic.
As you say, patience and thinking about all the variables. A bike should be given the space of a car, if I'm given half the space I tend to accept that, less and I get miffed. Cyclists are quite squishy and metal boxes aren't, you tend to remember that when one is close enough to you for you to consider it dangerous and react accordingly.