look for a dsg specialist in your area and read their reviews first... And before you book the car in read below:
I know it sounds stupid but your problem might be coming from the wrong oil used or to much/little oil in the box... these automatic gearboxes need a special oil that have extra chemicals added to promote non slip, anti corrosion and anti foaming... plus it needs to be put in at a certain heat... now the first time i did mine i put in new oil after i drained 7 liters of oil out... so all came out apart from the 500cc that was in the filter, I got that out when i dropped the filter out too... than i put in a dry new filter... filled it up half way turned the car on filled it up completely.... went for a drive... it did the exact same as you are describing....
got back, opened the fill plug and got out 3 liters of hot oil... left it like that for a day and it drove fine... attempted to fill it some more the next day with the 3 liters and it has been fine since.... somehow the thing doesn't like being rushed... ( cold oil duh)
Now i used a syphon handpump. not a fancy gearbox oil drain and filling machine like most specialist do... and if you used one of them to fill the oil it should be fine... maybe they didn't replace the filter... now it's a screen filter and it can be skipped once every 30k but if you don't know when it was last done insist they replace the filter too... they have to drop all the oil to get to the lot anyway...
PS afaik yours already has the extra plates in there to simulate gearshifts so after having your multitronic ecu repaired all that can cause these problems is the type of oil/to much oil/ or to little oil... and the gearshifter itself ( the part that you use to select PRNDS) mostly it's simple dirt that can be cleanup with an electrical cleaner... same goes for the extra plug you got going to the gearbox.. it can be filled with oil or coolant... an electrical cleaner (or brake cleaner) can help clean it out really quick and safe you ££££ so if i was you i'd start looking at what you can do yourself first, before spending loads of money...
PPS yes i sorted my multitronic out myself and saved ££££