Toddler goes free. Just use the wide gate and have the toddler pass through with a paying adult.
Contactless is the easiest way to pay. Tap in and out with a contactless card or using your mobile phone if you have Google Pay or Apple Pay set up.
Your teen needs to pay. You can give them another contactless card to use (one of yours, just not the same one you're using to tap in and out) but they will be charged full fare.
Or you could get a Visitor Oyster Card (order online or some places outside UK - check the TFL website). Once you arrive, ask at a tube station kiosk to add the child discount to it for half price fares. The card costs £5. Credit never expires so you can save it for future trips to London. Or you can return it when you leave at a machine and get a refund including unused credit. Just don't preload with too much credit because over £10 unused credit means sending it off to process a refund which is a faff.
Query whether it's worth the hassle for 3 days. If you're only travelling within zones 1-2, the daily capped fare for adults is £7.70 I think. Think it's £9 for zones 1-3. Half that for your teen if they have the discount.
So you're saving around £10 - £13 over 3 days assuming you can be bothered to return and refund the Visitor Oyster Card.
Depends whether you think it's worth it. If you plan to return to London, it probably is as the card doesn't ever expire.