Looking for 3-4 man tarp, tarptent, or just a plain tent.

I'd take the 2 man tent for you and one kid and tarp the others. It's cheaper, lighter and they will be well protected AND you can use the 10' X 12' "tarp for two" as a fly to cook and eat under in case of rain. Silnylon would be the lightest – and most 'spensive.

Buy Triptease cord for the tarp – two 50' lengths should be more than enough.
And practice setting it up in different ways. Look at the nice stormproof tarp setup illustrated on p.13 in the little paperback "Lighten Up!" by Don Ladigin W/ illustrations by Mike Clelland.

P.S. Remember to take a groundcloth for the tarp. Painter's plastic should last for more than one trip and you can decide on a better cloth if your kids like tarping. You may want to take a mosquito bar to cover their head area. AND some good repellant for all of you as well.

And do you have any lightweight tents now? You dont all have to sleep together

Watch steepandcheap.com for an Alps Mountaineering Lynx 4. $84 bucks. A little heavy, but………….

Sorry Trevor, I am pretty sure that TT is not ignoring you, just too busy trying to keep up with orders and organising new stock.
This is the result of having had the three busiest months ever.
Not an ideal situation from a customer's point of view, but it happens.
Franco
(not an official TT comment…)

Personally, I would go with a floorless tepee. Pretty light, just a cut out tarp. You can improvise a pole in the woods as well.

Not a recommendation just FYI
My Rainshadow took 2 weeks. Just received it last week. It really is a nice 3 person size though.

I've heard great things about the Hogback if you can find one. At this point, maybe getting lucky on finding a used one may be your best shot.

Otherwise, I would put your boys in your 2-person shelter and buy/borrow a solo shelter for yourself.

Put your kids in the tent and use an 8×10 ft silnylon flat tarp or smaller for yourself. (Make sure you get lots of practice pitching it before the trip.) A pyramid or shaped tarp would be a good but less general-purpose shelter too.

Check out:
Oware
Golite Shangri-La 1, 2, or 3 (whoever has it cheapest online, need trekking poles for 1 and 2)