I looked at doing this a while back and it’s easier than you think. There are small keypad boxes used to open gates outdoors. I think they were around $200. Relatively cheap and designed to sit outside.
So what if they use em 3x/week. They put all 3 tokens in your vac.. problem solved. But dang, if you have very many washing 4x/week, that's 17 washes/mo & costing you a $hitTon!