There have been many similar discussions involving 3/4 ton diesels towing various 5th wheel models. Most focus is on the towing capacity, which depending on your Tundra configuration and whether you have the towing package,
could be up to about 10,000. With a GVRW of 8600 for the 32Buds, and 1000# of clothing, cargo, etc, you'll be near the max.
Your payload spec is dicier. Depending on your Tundra model, you could have a payload approaching 1700. Assuming 1000# tongue weight, that leaves a bit of room for you and the family.
So as the kids grow, you'll be either near the limit, or a bit over. When these questions come up on the forum, there are 2 types of answers: one group says you need to stay within the specs to be safe and to avoid excessive wear on the tow vehicle. The other group says they're doing it with no problem. The comments on the Tundra forum are of the latter type.
I would mention that if you're planning on towing in the mountains, gasoline engines lose power as the air thins at higher altitude. So if you're near the limit, you might need to stick to the east coast, and maybe pick your mountainous routes carefully.
You might ask some of the people on the Tundra forum about the handling at highway speeds and in crosswinds. As tongue weight goes up, the balance of the tow vehicle can change, affecting handling.
I myself tend to go with the safety group, but I've had our actual weights measured and we almost exactly at our payload limit. And even though we have 1000# of margin on towing capacity, we probably need that margin because we drive through the Colorado mountains all the time.
So where you plan to go, along with some more specific feedback from Tundra owners may help you make your decision.