
The North Face
Wawona 6
Spacious vestibule, strong in storms, but rainfly tricky solo.

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Not sure if you mean 2-3 person in tent numbers or in real life numbers, but I have used an 8-person Coleman Skylodge for 3 adults in high winds and had no issues. It actually rained a couple of times on trips along with the wind with no issues as long as I staked it down with good stakes. Only has doors in front, but has windows on all sides.
I would go with a Coleman Skylodge Instant Tent, at minimum 8-person. I have the 8 person and the 4 person and they both are solid. The 8-person should allow for a queen size air mattress and plenty of room for "stuff". If you can swing it, the 10-person may be better because your family can grow with it as you need more space. I wouldn't get it directly from Coleman, they are cheaper elsewhere.
Yes, they make a 10-person Skylodge. I have only used the 8, and it wasn't hard to put up alone. I had it staked and up in about 4 minutes. The 10 shouldn't be much different. Instant tents are very convenient for set up.
I would stick with Coleman or Ozark Trail. I think they are in your budget range. Ozark Trail probably is best for your size/budget requirements. A Coleman that size is going to be a bit more. I have an 8 person Coleman that probably would get the job done, but with that many people, a 10-12 person might be better for you. An Ozark Trail model would run about $200, a similar Coleman would be at least $150 more.
I have used my Coleman 4 person for solo trips for about 3 years now and have had no issues at all. This includes a storm with 50 mph gusts. Besides the money, I think Ozark Trail offers more variety in design than Coleman, so that may fit your needs better. I cannot speak to it's durability as I haven't had any personal experience, but everyone I know who has one is a fan.
I have the Coleman Skylodge 8 person we mean to get the four. It is such a breeze especially when moving camp sites too. Only caveat is its size when being packed. I just throw it on the roof rack.
We have the Coleman 8 person Skylodge. It has plenty of ventilation to limit condensation. It’s easy to set up and price fits your budget. I can’t speak to the fit when using cots, we camp with a queen and a twin air mattress and it has room to spare with 10 days worth of gear.
Try Coleman Skylodge Instant tent. Extremely easy to use. Only downside is occasional leakage.
I've got a similar issue. I've got 2-3 tents that I've narrowed down to but haven't pulled the trigger. For size, it really depends on if you want lounging space inside. A 3-4 person tent is good for two adults with gear inside. If you want to set up chairs inside then a 6 person would be better. With a 4yr old you might even be able to get away with a 4 person but a 6 person would allow for growth. Coleman and Kelty have a lot of nice tents that would be fine for what you want. A Skydome with the screen room has the vestibule for a reasonable price. Not to mention being a darkroom tent so you're not having to wake up at first light. Something like the Coleman Skylodge would allow you to walk around inside. If you want to use cots then bigger might be better. I went solo camping with a 4per dome and my cot took up most of the space. There's no chance to fit a second one in there for sure.
I've used 4,6,8 man Coleman Instant Tents for years. Goes up in about 3 minutes, comes down in about 8 minutes (you have to roll it and smash it back in the carrying bag.

The North Face
Wawona 6
Spacious vestibule, strong in storms, but rainfly tricky solo.

Gazelle Tents
T4 Hub Tent Series
Fastest setup, durable, but bulky and awkward door.

Durston
X-Mid 2
Ultralight, spacious 2P, but not for very strong winds.

Durston
X-Mid 1
Budget ultralight 1P, spacious, but large footprint.

Naturehike
Mongar 2 Backpack Tent (Nylon)
Budget 2P, spacious for price, but not for 4 seasons.

Ranked #1
Durston - X-Mid 2

Ranked #1
Gazelle Tents - T4 Hub Tent Series

Ranked #1
Gazelle Tents - T4 Hub Tent Series

Ranked #1
Durston - X-Mid 2

Ranked #1
Durston - X-Mid 2

Ranked #1
SlingFin - Portal 2