Our situations are very similar!
Max, my golden retriever, has attended training classes from being a puppy and is now 19 months old. When he went into the adult classes I thought it could be something Sapphi, my lab who is now 3 but was 2 1/2 a the time, could do too. Sapphi, like Tilly, was a little wary of strangers despite having the same socialisation as my other two dogs, so I thought it might help her too. So we took her along too, my OH comes training with me and we alternate handling each dog every week. Sapphi's confidence has grown so much and its so lovely to see a girl who wouldn't approach any of the other owners now go bounding up to say hello and take them balls to throw for her in the play sessions.
I won't lie, sometimes keeping their focus is a bit more difficult. The problem we have is that all our dogs work better for me, hence the reason we alternate dogs. This is because apart from going to training classes my OH hasn't ever done any training with them. Before we took both dogs he just sat and watched.
So sometimes if we are working off lead in a group situation I'll give the one I'm handling a command and the other responds too. I firmly tell them "away" and then ignore while OH gets them back under control.
But its not such a massive problem, you just have to work a bit harder to keep their attention on you. I've certainly not felt it such a problem that I would consider not taking them to the same class.
Thats my experience, my advice would be give it ago and see how it works out for you. Hopefully you'll find Tilly gains in confidence like Sapphi did.
