No, something is wrong.
I tow with a 1.8 Astra auto, it'll hold top on the flat without any trouble. With all the power from a 3.0 you should be able to hold top even on slight uphill gradients.
Firstly, check your tyre pressures. If they're low that'll cause extra drag.
Then get some Redex Injector Cleaner. Use 75ml in a tankful of fuel. If the engine runs smoother afterwards, solo and towing, that would indicate that the injectors were sticking. Continue using Redex at 1000 mile intervals to keep the injectors clean.
It might be worth changing the auto gearbox fluid but some Omega autos don't have a drain point. You may need to seek specialist help but don't assume it's the gearbox, it could be the engine down on power.