How many of the children can you fit in one bed? A popup worked for my family as us older kids left and it got down to Mom, Dad and the three youngest girls, six year age range. The popup was a 12-foot box, roughly queen size at one end, full bed at the other. The three girls "camped out" together in the big end. 1970s, cold-water popup with minimal kitchen, thus really a big tent up off the ground.
Big family to accommodate, you'll want as much seating as possible (for rainy days), an adult end and a kids' end, so I recommend a double-dinette model like Jayco's 1207 floorplans (currently Jay Series, similar floorplan has been other model lines in the past). They currently offer a two-dinette in a 10-foot box (1007) but that has almost no space for six people to move around. The 12-foot box model (12UD) in their cold-water Sport series has similar space, and it will be lighter and less expensive, but not by much. Starcraft (Jayco subsidary) will have equivalent models.
Similar from Forest River, would be Rockwood Freedom 2270 (Flagstaff Mac 227).
I've not shopped other brands (Fleetwood, Viking, Coleman) since I have no dealers for those.
If you want a bathroom, particularly with a shower (which can be nice for just the two of you), selections get more difficult. Forest River is still making bathroom models, but the bathroom takes up a lot of living space, even if you move up to a 14-foot box with the dinette in a slideout. Most bathroom models are single dinette, but Rockwood Premier 2517 and 2716 at least provide a sofa for additional seating.
When popups get this large, they can be heavier and often more expensive than small ultra-lite travel trailers, particularly hybrids which might give you a real bathroom and kitchen, putting the beds into tent pop-outs at one or both ends (like Rockwood Roo, but almost everybody makes a line of these).