
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.
Like you, I had a Coleman pop-up for 12 years with no issues. I am also worried about the quality now. I got the Blackberry Skylodge and the poles snapped. It was an awesome tent tho, the bug doors were so nice. I didn't like the T4 for the reasons I mentioned. I now do not have a tent and no clue what to do.
Honestly, I considering getting the same tent. I am just worried about reports that it is not the same quality because it is more money. It was a main pole. I was folding it, like I have done a 1000 times and it snapped.
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.
You're getting into a new hobby. Don't drop thousands of dollars up front. Buy a Coleman 3 season tent to start. Same goes for the sleeping bag, just get one with temperature rating 10 to 20 degrees Fahrenheit less than what the daily low is said to be. If your not hiking into the campsite get regular camping chair and cooler. Same goes for a sleeping pad. Get a heavily well reviewed sleeping pad. If I was in your shoes and your okay spending a little bit of money. I'd just go to Walmart or Academy sports and buy a tent, bag, pad, and chair there, if car camping. If you wind up enjoying yourself, use the tent and chair until they quit and then upgrade. Buy a better sleeping bag and pad once you know you're enjoying camping. Waking up well rested helps you enjoy the experience more.
X = number of people camping, Y = rating of the tent. X+2 = Y for gear space, and a vestibule for inclement weather cooking is really nice. Looking at the tag on the tent we bought a Coleman three season to use camping at the Grand Canyon, it said 8, we had 4, it was just right for size. I've camped two in tent meant for 4, it allowed a cot and stored our gear inside with us. I've moved on to building a DIY camper and keeping that in mind. Queen mattresses and 3 bedrooms are a bit much.
Keep in mind the rating for how many campers is effectively half of the number given. We bought a Coleman for 8 and it was reasonably useful for 4. If car camping - not backpacking - weight is less constraining so choose for comfort.
Tents by nature leak. Its not necessarily better using treated poly fabrics vs the old canvas, either, and the mountaineer designs for low profile in high winds haven't made them a easier habitat as I got older. I miss the old tan cabin tent we first had vs a two man pup tent with no rain fly. Seek out what features you need, not what Brand. Rate the occupancy by half their rating as its a tight survival stack for the most part. If you want a 6 person it will do well for three and leave some room for the packs or other gear out of the weather. For a truly 3 season tent then it can't have a large screen dome which is great in hot summer weather but not very warm in late fall or early spring. We went to the Grand Canyon in early June one year, took an 8 man Coleman for 4, and the lower wall vents were wide open in that design, 48F in the morning was not anticipated on the South Rim. There was nothing to close them up. That kind of feature is more important than a shore power port or a hanging mesh net in the center. Shop the features and then let what model fall into whatever brand is credible with a good rep, the dozens of new Chinese tent brands that last 90 days aren't necessarily a bargain when it has no longevity.

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

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Gazelle Tents - T4 Hub Tent Series

Ranked #1
Gazelle Tents - T4 Hub Tent Series

Ranked #1
Durston - X-Mid 2

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The North Face - Wawona 6

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SlingFin - Portal 2