No, they are WAY too young. Its not just the responsibility aspect. Cell phones create very independent children - their friends don't call on the land line, you don't know where they are when you call them...7 and 9 are too young for that kind of independence.
But cell phones seem to be the least of the problem here. I don't envy you, Eyebrow - I had to deal with a difficult mother when I was bringing up her child (me the stepmother), and it was a nightmare. I don't like what this woman is doing to you - but you didn't ask for advice on that aspect, so I won't give it!