Yes, teat tape works, as long as you check it frequently to make sure they haven't managed to work it off.
Last year, my dd's 4-H doe had to be penned with her kid at our small community fair. Her wether kid managed to get the teat tape off of one side during the night before the show, and dd had to show a doe with a very lopsided udder. <argh> Her doe, who had a lovely udder normally, was placed at the bottom of the class due to this. It was hard to hear comments from the judge about the "poor udder on this doe", when we knew it was because one half was normally full, and the other half had been nursed out all night, but what are ya gonna do, eh?
If you keep the kids in the other pen and have mom teat taped, I doubt she'll stand there long enough for them to get the tape off.
Oh, and save some money on that teat tape - the product is Micropore paper tape, and is available in any pharmacy or medical supply house for less than the cost through Hoeggers, Jeffers, etc - and NO SHIPPING costs. I ordered the teat tape, and at $5 for 2 rolls + shipping, it was pricey. Also annoying to me to find out it was the same stuff I use every day on the job (I'm an RN).

I had a whole lot of the stuff sitting around the house - it tends to come home in pockets at the end of the day.