My wife had experienced a problem with the automatic gearbox though her description wasn’t the best but I’ve now experienced it so it needs sorting

What happens is this; when the gearbox goes to change up a gear it seems to get stuck in between gears and the engine revs up, then when the gear engages (with a bump) it displays ‘AUTOMATIC GEARBOX’ and goes into safe mode, i.e. high gear and manually having to change down.
So today I went to check the ATF. I drove it to warm it up then parked on the drive, jacked it up, remove filler bolt, lowered it down to level – doh! forgot to restart the engine, oil pours out

– jack back up quickly, start engine then lower car. Now no oil is coming out so I jack-up then top-up several times until it’s at the right level. Unfortunately I don’t know if the level was right (as it is now) but I do know from the black stain on my drive that the ATF is very dirty. Could that fact alone be the cause of my problem?
If it is what sort of cost is it to a) buy parts (ATF, filter, gasket) and where from (online, around Nottingham), b) get it done somewhere (again around Nottingham). My limited home facilities means it would be difficult to do here; but if the difference is a lot I’ll manage at home

If the problem’s something else I have a good automatic gearbox on my other miggy (with a poorly engine), how difficult are they to replace? Doubt I can do it at home though

Cheers.