Depending on what sort of drama course she wants to do at uni makes a big difference as to whether UCAS points matter or not. If it's a drama school she wants to go to, UCAS points won't be a huge deal - it will be all based on paid auditions, and evidence of LAMDA qualifications will stand her in good stead.
If it's a theoretical drama course, which is essentially reading plays and writing about them, UCAS points will help a lot.
Alternatively, if it's a degree like the one I've just finished, which is a drama school style course in a university setting, it will be a mixture - UCAS points will be a consideration, but evidence of performance experience, a good audition and other factors matter a great deal more. It all depends on what your DD is looking to do.
Just to explain the UCAS points system - most institutions won't say "You need to get ABB", they'll say "You need a minimum of 260 points". They may make subject-specific requests, such as "A minimum of 260 points with a B in Drama", but aside from that, the points can come from anywhere.
So say DD goes for a course which requires 280 UCAS points, not subject specific. That's the equivalent of BBC. However, she could also get it by getting ABD, which is also 280 points.
Or, if she was to get BBD, so 260 points, but then get a Distinction in a LAMDA Grade 6 exam, that's an extra 40 points, taking her up to 320 points and meaning that she meets her offer and gets in.
There's an explanation of how LAMDA converts into UCAS tarriff here
Monologue experience will really be of use to her when it comes to university auditions - you can't audition in a duologue. Maybe at the meeting, suggest that this time, she does the monologue, but demand that next time, she is allowed to take part in the duologue for UCAS points purposes?
It sounds like the other mum is jealous, especially if she is a pushy performance parent, and knows that your DD is hoping to carry it on to university level.