Yeah, I'm on board with those who say that since you gave her free reign you're sort of stuck. And you certainly won't be the first or last to have people at your wedding that you don't know from Adam.
However, if I were in this situation with my own mother, I think this is how I would approach it. (Keep in mind that I had a great relationship with my mother so whether this would work for you or not depends.)
Mom, you know, thinking about it, I'd really like to invite best friend's adult children although they weren't on my original invitation list but the budget is at the limit. Is there any way you could contribute extra to the wedding so we could include them?
This is asking for a favor without bringing up the fact that you're not thrilled with the people she wants to invite.
But to look at it from a slightly different angle, I am wondering how many people we're talking about as far as the best friend's adult children go, six, right? When figuring your budget, are you figuring the cost per person of everyone you've invited, or of the total number who are likely to accept? There is always a certain percentage of people who will not attend and these six might not actually throw you over budget after all. Also consider the fact that the people who you don't know also don't know you, and are less likely to attend for that reason.