IMO for under 10k new you are probably going to be getting Chinese imports. Mixed reviews on the those. For just a smidge more you can start getting the entry level Aussie built ones. I am sure everyone will tell you their thoughts on Chinese imports.
Look at your needs carefully. Just because you’ve got 3 kids doesn’t mean you ‘need’ acres of canvas so you could stick with a 10’ or 12’ tent. More canvas means more poles, means longer set up and set down times
We’ve got 3 kids under 10 and bought a second hand rear fold soft floor. Youngest sleeps on the floor and we’ve offloaded the two older into an oztent or swags. Our set up is 20-40mins depending on how much the kids decide they suddenly need us to do super important things right there and then. BUT that definitely won’t be everyone’s cup of tea because the amount of interior canvas space is minimal – but it suits us just fine.
Re the Chinese campers: Every one I’ve seen seems to be ok for tent set up, but relies on x100 poles to set up the awnings. Friends of ours (first time CT owners on a budget) have 3 kids and just bought a Blackseries camper for $8k. You’ll get mixed reviews from other swaggers one them, but they’re very happy with their purchase. We watched them set up for only the second time ever - The main tent is a 12 foot and it’s not too bad to set up, but the awning had eleventy million poles and spreader bars and it nearly caused a divorce. I’m sure with more practice that time will improve. But having numbered poles that have to go in specific positions would be too much work for me, and get old pretty quickly. It might not be an issue if you are the type of campers who go to one spot and stay there for a long time. We mostly tour, usually moving every one or two days, so easy set up and flexibility is required.
Other friends have a Leisure Matters bought from Sydney franchise. It was delivered missing some awning poles which the company couriered out to them. Again they’re very happy with it. The eastern state franchises have closed down but there’s still one in WA. They set up and pack in about the same time as we do. Again they are happy with the purchase. On our last trip one of the bolts holding a brake caliper came out and we had to cable tie it. But that could happen to anyone really.
Now. if it was me… You’ll find lots of good second hand campers for that price usually with a few more bits a pieces bolted on by the owners. ( I missed out on an older Off Road Cub Off with nearly new tires and brand new canvas that was $8000, and a hardly used Camel Discovery for $5k. ) You’ll also find entry level campers that are being sold nearly new as the owners have decided it’s not for them.
At the end of the day, if it works for you, go for it.
Another alternative is to get a trailer place to build you a standard box trailer and bolt an Oztrail Camper Trailer Tent on top