No. No, No, NO!
There is a reason that the coaches have brought the group back to the very basics.
If I am being frank, the frustration that your daughter is feeling right now with not doing the skills that she was doing in rec classes is a large part of the reason that so many gyms have what seems to be an age limit for their JO compulsories. It is a tough adjustment for kids that have been pushed through skills with incorrect technique and improper form to be thrust into a preteam or team group at a gym that focuses on strong basics. Also, it is more difficult to "unlearn" bad habits than to teach the skills from scratch. It is much simpler when you are working from a clean slate.
That said, if the coaches have chosen her for preteam, they obviously see potential in her and feel like they can mold her into the type of athlete that they want her to be. You just need to explain to her that there is a difference in doing a skill and in doing it correctly/well. Maybe have her take a look at the skills that she was doing (I am sure you have video of some of them) and then have her watch the level 3 and 4s in your gym do the same skills.
The toughest part of this transition is going to be getting her on board with the JO philosophy of details and perfect technique and out of the recreational mindset of simply acquiring skills. The bigger skills come from a strong base. You can't build a skyscraper on a shaky foundation.
Long winded way to say... Continuing private lessons with the previous rec instructor will reinforce the poor technique that she has already learned and will slow down her forward progress in her new group.