1. Record your student's lessons. This can solve a lot of problems about "What the teacher said." There won't be any argument, because you can simply watch the lesson back and find out exactly what the teacher said! This also will help you catch details that you didn't in the lesson, and it may help your child evaluate themselves more objectively by watching their lessons from the outside.
2. Take notes during lessons. As a teacher, I've observed that my young students who remember the most are the ones whose parents supplement my practice charts with their own notes. After all - parents know their children far better than I do. They know the little detail which I will take for granted but that they know their kids will forget, they can clue into a new way of explaining things that is particularly effective, or a subtle change in their child's mood that I might miss. This will also help you have a record of the lesson at home.
3. Read the book Helping Parents Practice, by Ed Sprunger. This book is amazing and my parents who have read it and used the techniques have found it to be invaluable in helping them understand the nuances of practice as well as how to help their child navigate the violin.
4. When you're setting up your child's practice area, make sure to include a comfortable chair for yourself - somewhere you will enjoy sitting. Add your favorite pillow, a comfy throw, and anything else you want to make this a warm and inviting environment for you.
5. Stock your favorite blend of coffee, tea, or beverage of choice and sip on it slowly while you practice with your child. Pick a music themed mug or just a mug that you like. I confess to using this one on occasion when I teach...(Disclaimer: I stole this idea from the Ed Sprunger book. It's seriously THAT good!)
6. Schedule practice as part of your day. I would estimate that 80% of practice stress for parents comes from struggling to fit violin practice into a day full of work, wrangling kids, and errands. If you know that practice will come as soon as you get the kids home from school and before you make dinner, you'll be much less stressed.
I know some of this seems like more work for parents, not more fun, but I promise that incorporating these ideas and strategies into your violin routine will make for less stress overall. If you know you have reliable records of the lesson content, a scheduled practice session, a great place to sit with your favorite beverages - and these great suggestions (Creating Enthusiastic and Independent Practicers Parts One, Two, and Three) for helping your kids enjoy practice more, then practice will be much more fun and much less stressful for parents!