As far as I'm concerned, fixing a brolly to my chair is a hindrance and restricting so I wouldn't use such a thing...
Generally speaking I only see a brolly as a means of keeping my gear dry and I only sit under one if it is really heavy persistent rain, but even then I am always far enough forward to allow a decent cast and I also wear clothing and boots to allow this.
That said, I usually adjust my fishing to suit and if float fishing I will always fish closer in (which I like doing anyway) use a centre pin and cast under arm, or more, just 'lay' the float on the water.
The important thing is to have sufficient space for an unrestricted strike - surely the most important factor - and one that is not impeded by the edge of a brolly!!
Fishing in the rain IMO, is a state of mind in the first place, and if hassle with umbrellas, getting wet and being miserable is not your thing to begin with then best not to go out. Personally, I see it as a challenge and I do have to adjust to moving around much slower and being more deliberate in my movements, but once settled in my swim I quite enjoy the different kind of quiet it brings......
It must be said that being at peace with adverse conditions mainly comes from the walking I do throughout the year in all weathers, when you cannot base regular outings on what the weather man has said the night before. When I want, or have to go, I'm off out regardless and all the better for it on my return.
No, my advice is to try and embrace the conditions rather than fight them. Adjust your fishing to what is comfortable, don't try to do too much, buy a brolly that works independently to your chair and away you go!!
Either that, or stay home!!!
ps Doesn't always work though, and packing up in the wet stuff still a real bind.............................