Hi, welcome to the forum.
I can't offer you specific advice on the reverse problem but it might be a solenoid problem. Someone with more knowledge will no doubt be along shortly.
A lot of issues with Omega autos come about from lack of maintenance. They need an oil change every say70k miles depending on useage. There isn't a handy dipstick and the level plug is tucked away under the drivers side of the car halfway up the box. Changing the oil is "easy" enough but can be messy and involves removing both sumps off the G box. It is also as well to change the filter at the same time or clean it at a min. gaskets and filters come with a forum discount from an outfit called JPat. (I got mine from them, nice fast turnaround)
One question is do you get any weirdness on the selector lights on the gearchange during the reverse problem?
Changing a gearbox. I have done this twice on my car and it is fairly straightforward BUt the gearbox is very heavy about the weight of a hefty bloke. Unless you have a lot of trolley jacks etc I would always recomend using two people.
Now the diesel and 2.5 petrol Omegas use an AR25 auto box. They are on the limit for the torque of a diesel and the ebst way forward if you are changing gbox is to obtain anAR35 as fitted to the 3 litres models. Price could be anything from £50 to £150. There are several breakers on the forum and they would be a starting point byPM message as you haven't enough posts to do a wanted Ad just yet.
There are some good guides including checking gearbox oil level in the maintenance guide section. That as a minimum should be your starting point.
