OP,
We live in a >1200 with two adults and 2 kids and a cat and there is room for another couple of people (prob 1 adult or 2 kids) still.
I am still figuring out storage solutions to stuff (we moved at the end of summer) and wish our kitchen was bigger, but, some people CHOOSE to have a smaller home. Most of the people I know with children and large houses have kids in school/daycare and both parents work full time to make ends meet. I wanted to stay home with my kids and raise them myself (no offense to to WOHMS if that's what you want), so we choose to have a smaller house then may be the 'norm' (I'd say it's small for the area we live in...BUT...it's about the same size as the one I grew up in, in a fam of 5, so I think that makes a diff too).
We could have bought a bigger house and a much smaller yard, but we wanted that place for the kids to play and run and build and climb and explore. We could have bought a bigger house with the acre we have now, but it would have been stretching it. I like knowing that we are not in danger of not being able to pay our bills. I like not fighting about money, not having any debt besides our mortgage. We don't like spending every single last penny each month, or living beyond our means & wracking up debt just to have a huge, new, lavish home. Our home is a good size for our family, even a bit roomy (and I'm sure we'll have more kids), and it's clean and sometimes tidy, and warm and cozy and full of love and happy parents who can pay the bills and still put some into savings.
Reading your post, I wonder if you chose the house you're living in now, or if you feel like it was your only option at the time? And also if YOU'RE ok with it, but you are feeling sensitive to what other people may think of you, incl your children... Your motives may help clarify what the best step from here is.
I see three options: Stay in your current home and make it your project to make sure you are using each space wisely (I second the suggestions about things such as futons, which can pull double duty--or a storage chest you use for a bench at the kitchen table (double duty) etc ) and making it the homeiest home you can with things as streamlined as possible (we are still very much getting there ourselves). Or, move to a larger house. Or move to a house a similar size as your current one, but with a better layout or that you just personally 'like' better.