We had 2, and I was desperate for a 3rd for ages - but got my head round it as i had been ill having ds (dc2) and dh was really not keen.
Just when I got my head round it my mirena coil fell out and I got pg with dd2, now almost 5 (ds is 22 months older, dd1 2 more years older). I had 3 under 4, it was bloody hard work for a while, but worth every moment.
I was seriously unwell during and after pregnancy with dd2, had 30 hospital admissions in 3 years for a kidney problem. Still bothers me sometimes.
But now ... wow! We have 3 children in school. They play well, they have fun, they end up sleeping in the same bed! We had a holiday this summer that involved us going to London and Paris, taking in the sights, museums, art galleries, etc - all the stuff dh and I would have done alone. They are fabulous! I love watching the different relationships develop, though occasionally feel sorry for ds with 2 very strong willed sisters!!
I seriously love having 3 kids. Even with all the struggles and pain my kidney stones have caused, I never for a moment wish we hadn't had dd2. We would never have had her if it had been our own choice, but we really feel she was meant to be.
Like OP, we had thought about the snip after ds, but I wasn't sure enough. He did have the op, and while I was still pg with dd2, as my doctors had said another pregnancy would mean I would lose a kidney and could have killed me.
When they are little you don't need a people carrier - if at all. What did people do before people carriers - you just all crammed in the back of an ordinary car! For the first 2 years at least you dont need extra rooms, and now we have discovered the delights of Youth Hostelling where we can easily get a family room, or self catering.
I don't agree with the people who say "well you might as well have 4". I didn't want 4. I am happy and delighted with my 3!! Don't let people put you off if you and dh really want another - it is worth it, it really is!