What is it, some variety of Cotoneaster? You've not said...

Deciduous Cotoneaster leaves usually turn red before falling in autumn. Mine haven't started to turn yet though. No idea about pruning though, I just cut off whole branches when they get in the way.

I would doubt you can turn that cotoneaster into an umbrella shape, it simply isn't the way it grows.

When I first saw this I thought it was a 'top-worked' Cotoneaster dammeri; so it would be semi-evergreen. There is a variety which is made into an umbrella shape which is Cotoneaster Juliette‎ but this is variegated. I am of the same opinion as MG; the stems, unlike the Salix caprea 'Pendula' (Kilmarnock Willow) the branches aren't strong enough to give the umbrella shape.

OK, let's see if I am sussing out the present structure of this. What I am seeing is an upright trunk, with a trailing Cotoneaster grafted on top, with several strong branches running straight down along the trunk.
I'll admit that that is not a promising beginning, Amsterdam, especially since the trunk has been allowed to come loose from the stake and curve. Straightening that trunk has a high priority, but it may not be possible, now that the trunk has developed that much caliper. Are you sure that it has only been one year, Amsterdam?
Aside from the trunk, the next step is to remove about 1/2 of the length of those vertical branches, cutting back to side branches. The goal is to encourage new growth at the top, since, in the long run, none of the present main branches will be part of the main structure.
When those new branches start, it will need to be necessary to use spreader sticks to keep them from falling down right next to the ones already rejected.
All in all, it will take about 4-5 years to salvage this.

Thank you all for your various replies. I will give it a trim as Tugbrethil suggests and see how it responds. Lets just say it is a work in progres....