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

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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.
Coleman 10 person lighted. Have to get it when Costco stocks it, but it’s a solid tent
My setup is a 10'x20' Costco carport with a Coleman 10 person pop-up tent inside one half (with mesh windows zipped), and the other half of the carport has a rug/carpet floor with a table, a couple chairs for a simple living room of sorts. All under $500.
We use a 10 person Coleman instant tent It is easy to set up and break down, it does have two separate entrances, you can put a rainfly on it but any tent is as waterproof as you make it.
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.

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
The North Face - Wawona 6

Ranked #1
SlingFin - Portal 2