New Ongar to Barnhill Road

You've ignored both points that I made.

The current road could be widened and straightened quite easily. Road safety isn't a justification for an entirely new road, especially one through a public park where you get many pedestrians and cyclists. So, it all comes back to what exactly is the justification for the new road?

Roads or traffic levels in themselves aren't dangerous. It is driver behaviour that is dangerous (but this is pretty much irrelevant in the context of the discussion anyhow).

Widening and straightening the road could have an impact on residential properties, I am not familiar enough with the road to know.

So why make a point on something that you admit not being familiar with?
For reference, I am familiar enough with it as a driver, a cyclist and as a pedestrian! Now I'm not a civil engineer but I am somewhat familiar with how road widening practices are followed.

Secondly, using the existing road brings it into Lucan village and the congested mess therein. The alternate through St. Catherine's Park was designed to avoid that.

So what exactly is the purpose of the new road? Is it to facilitate new housing development or to link the N4 & N3 reasonably close to an eight lane motorway?

Either way, the purchase of extra land beside Catherine's opens up the possibility of repurposing some of the existing park for the road, while still maintaining the same size of amenity.

This moves the park further away from the existing residential access points meaning that if people want to walk there, there is an increased likleihood that they will use a car.

Plus a significant amenity to the existing park is along the river. Are you seriously thinking that a new road won't affect that or that because some land further north has been provided that it is a meaningful substitute?
Using your logic, the council could soon decide to buy more land even further north on a continuous roation and eventually the entire park will be north of Clonee?

I'm not sure of the plans you are referring to but if the council were to connect the canal to the park (which are separated simply by the rail line), then they would need to ensure that the surface along the canal towpath is sufficient that all users can use it. But there is no plan to upgrade the towpath surface and it will remain as a rough surface unsuitable for most bicycles, buggies, wheelchairs, etc.
There may be a pipe dream that embellishes a council document but there are no plans to my knowledge.

Anyhow, adding one end of a bridge into the park is not the same as my point about moving the park further north to use your logic!