Your earlier post about traveling from Venice to Paris said you will go by car. Has that changed?
If using public transport, I want to correct one thing posted above. The Family Card provides free travel for children under 16, not for kids who are 16. So only your 12-year-old will be covered.
I previously recommended the apartment in Chalet Fontana in Mürren at 245 CHF a night. Did you try there? If you are using a search website like booking.com it would not show up, so here is their website:
Regarding Wengen, it is a nice village, a bit larger and less charming than Mürren. The two villages sit high up on slopes on opposite sides of the Lauterbrunnen Valley. You do not see as many stunning peaks from Wengen as you do from Mürren. But it is an easy hike up to Kleine Scheidegg from which you will have great views. You can continue on the trail to Männlichen (one of the walks recommended by Shoe) but the peaks will be behind you, so remember to stop and look back, or walk the trail in both directions. Or better yet, ascend from Wengen to Männlichen by the "goat path" or cablecar, and walk toward Kleine Scheidegg and then back down to Wengen.
For other activities you will have to travel from Wengen, which means taking the train.
You will have the widest range of activities your kids will enjoy at Grindelwald, such as the Trottibikes (mountain scooters), the First flieger Zipline, Rodelbahn, etc., but all of these activities cost money, and it will add up quickly. Hiking is free, and Mürren offers the most hikes right from the village, without using lifts or other transport. That is one reason we favor Mürren. We are going back this summer with our adult children and grandchildren.
You can also rent bikes at Mürren and ride down to the valley and around, but you will probably want the cablecar to get back up.