As you're likely to be ferrying yourself and children around I would suggest getting yourself (along with your car) to either an auto-electrician or a large(ish) branch of Halfords. I wouldn't normally recommend Halfords, as they have a habit of not understanding the A2's quirks, but for electrical work you should be safe.......
......However.....make sure you keep a close eye on your car, and advise them how to access the engine bay (i.e. make sure whoever is going to check out your car understands exactly how the bonnet is removed).
Also, depending what options you have fitted in to your car, the alternator part number differs.
I'm sure there is a code for the alternator in the options list in the front of the owner’s handbook (this list can also be found in the boot near the battery). If you’re not sure how to “read” what the codes refer to, post all the codes and someone will decode them for you.
I wouldn't have Halford's perform an alternator swap, but their auto-electricians should be able to troubleshoot what is causing the alternator waring lamp to flicker.
It might even be worth a visit to a main dealer, fluttering your eyelashes, and asking if someone would be able to give you some free advice as you don't want to be stuck with young children in the car......you never know......maybe you'll find a kind tech who's happy "living the dream".
Silver 2002 1.4 TDi SE
Heated Red Sports Leather 4 Seat Interior, TTS FBMFSW, Open Sky System, Bose, RNS-E with Audi Bluetooth Telephony & SDS, DIS, Audi iPod link, Cruise Control, Komfortblinker, New Style Asymmetric Key Fobs, Rear Cup Holders, 4 x Electric Windows, Auto-dimming Rearveiw Mirror, A2OC Mats, TT Pedals, Puddle Lighting, Headlight Washers, Headlight Protectors, Debadged, 0.659 5th Gear, H&R Front and Rear ARB's, Koni FSDs & Weitec -30 Springs, Rear Disc Axle Conversion, ATE Powerdisc and Ceramic Pads, 17" TT Ronal Wheels with 215/40 Tyres, Floppy Wiper, Votex Body Kit, Spacesaver, Heated Wing Mirrors, K&N, Stealthed & a Coat-Hanger!