Excellent, Good News!
My number one piece of advice is to keep doing the "calmly". The "sometimes not calmly" is not going to score you any points. If you get frustrated go in the car. close the windows and doors, and scream at the trees.
#2. "complete protein" is a misconception or maybe even a myth. It was accidentally started in the 70s and its amazing how persistent a myth it has remained. There is an article, linked at the bottom, that is well worth reading. but i don't think using it as a argument will be effective. It's pretty technical. Plus it's one of those "everything you know is wrong" discussions that people just have to be ready for.
Also like most myths there is some truth to it. We vegans tend to dismiss it. Well after the hundredth time of "Where do you get your protein?", we get pretty tired of the discussion. But for some vegans, protein consumption IS a concern. So I think a better tact for your parents is not the, "All plant foods are complete protiens" but the "this is how I get my protein."
I think I may have mentioned CronOmeter to you before. I seem to bring it up in almost every thread. But if not, real quick, it's a web-based tool. It's not that hard to use, but there is a learning curve. It isn't very steep and after a few days you should be able to input your daily meals in less than 5 minutes. The website is free. There is an app you get if you pay to become a member. Plus the membership unlocks some cool features. but you certainly don't need to pay for it. Oh, and its just $3.
Anyway, the thing that separated CronOmeter from almost every other "calorie counter" is that it tracks amino acids. There are a couple of amino acids that are trickier for vegans. And Cronometer can show you if you are deficient in any particular ones (and with color-coded graphs). It's also a big plus that it tracks almost every other micronutrient that you need or can think of.
Another thing you can do with Cronometer is "fix" your diet. For instance, let's say that you see that you aren't getting enough of the amino acid lysine. Just Google "lysine AND vegan" and you will get a list of lysine-rich plant foods. then just add them to your meal plan. (BTW, Lysine is the reason vegans need to eat beans)
I'm a bit of a geek and like playing with CronOmeter. but if you don't have the patience I have two other recommendations.
Another web-based tool is SparkPeople. It has almost all the functionality as CronOmeter. it's more complicated, but its also more comprehensive. One thing that it does do that is very cool is with a push of a button it will make a daily (or weekly) custom made meal plan Just for you. It does not do vegan. but it does vegetarian. And your mom might like this: Another push of a button and it prints a shopping list. It also has recipes for all the meals it recommends.
Spark has its own free app. if you buy a food that has a barcode you can take a picture of the barcode and it enters it into your meal plan. Super easy. It also has a ton of other stuff. Forums, exercise plans, recipes, articles.
Spark and Cronometer also are compatible with many fitness trackers and fitness apps. so it can figure out how many calories you used more accurately.
My final recommendation is Dr Gregar's Daily Dozen Checklist. There is an app for it but you can also just print it and put it on the frig. I'll include a link to a PDF of it. You print it out and get it laminated. put it on the frig with a dry erase pen and each day you just check the boxes. At first glance, it looks like a lot of food but you have to look up what a serving is. Although some are pretty straightforward, some servings are just a half or quarter cup.
Regardless of whether you choose to use Cronometer, SparkPeople or Gregar's checklist, share your progress with your parents. Maybe even on a daily basis. the checklist is probably the easiest to share. Just put it on the frig. Cronometer allows you to print out a weekly one-page summary. Your mom might want to join SparkPeople, too. It can be a helpful tool for anyone concerned about nutrition - not just vegetarians. Give her your username and password and she can literally look over your shoulder.
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Protein for Vegetarians
https://michaelbluejay.com/veg/protein.html
CronOmeter
https://cronometer.com
How to use Cronometer
SparkPeople
https://www.sparkpeople.com
How to use the SparkPeople Nutrition Tracker
https://www.sparkpeople.com/resource/videos-detail.asp?video=17
Dr Gregar's checklist PDF
https://veganuary.com/wp-content/uploads/2016/07/Daily-Dozen-Checklist.pdf
Dr Gregar's checklist - serving sizes
https://www.mindbodygreen.com/0-234...ry-day-for-a-long-life-a-doctor-explains.html