That whole area is a total mess - council boundaries seem to have little regard for the actual settlement patterns or historic ties.
Personally, I'd reduce Stockton to just the areas north of the Tees. Then I'd give Middlesbrough its eastern suburbs around South Bank, Eston, and so on - the industrial belt between it and Redcar seems a fairly logical local authority boundary (though dividing up business rates from the site may be an issue). As Redcar and Cleveland would be somewhat short on population, I'd expand it into the North Yorkshire Council area to take in towns and villages that face towards Teesside rather than deeper into Yorkshire - places like Stokesley and Great Ayton as well as Whitby and Eskdale. I'd also put Yarm and Ingleby Barwick in here - meaning they are in an entirely Yorkshire based council, but one with a focus on the towns around traditional Cleveland, rather than one that stretches to distant Cowling and Drax.
The one issue is Thornaby which is clearly distinct from Middlesbrough, across the river from Stockton, and doesn't really fit in rural/small town Cleveland - possibly leave it up to residents to decide in a vote?
This subject surrounding Yorkshire comes up time and again, and for the most part, it is fairly irrelevant IMO.
The good people of Yarm want to be part of some resurrected North Riding from 50 years ago... So they want the quality of council services that they get over the border? The fact is that Yarm has much more to do with Stockton/Teesside than it does with Northallerton. Really, it is part of the Teesside conurbation, with it backing onto Eaglescliffe and Ingleby Barwick. The historic boundary in the north was the Tees but it was to get rid of most of the stupidity that it was changed in 1974. Not least in Teesdale where three of the major villages are south of the Tees but Barney and Middleton are north. Restore the old boundary... are we going to have bin lorries travelling from Richmond in order to serve those villages whilst another one races it up the other side of the dale? With the Teesside boundaries, it will never be perfect but I don't see that it's so bad. Redcar and Cleveland meets North Yorkshire in some very unpopulous areas, and you'll always have some challenges where R&C meets Middlesbrough (that boundary isn't too bad except near Normanby).
Perhaps the more baffling one is how Ilkley and Burley come under Bradford MBC. In terms of connectivity and geography, they are really strongly aligned with Otley and have little connection with Bradford, with Guiseley and Hawksworth constituting a Leeds enclave anyway.
The fact is that historically, rivers made up many county boundaries. However, that's really the worst thing you can do. Boundaries need to be in open land, with as few people bisected by the border as possible. Even in 1888, boundaries were redrawn in Staffordshire as people realised that having two different councils in towns like Tamworth or Burton was a really daft idea.