Yes, I do own a Honda Civic. As far as the space in back seat is concerned -- I think you can fit 2 booster seats and one car seat if they are the slim kinds (not all make and models). I am assuming you already have the car seats and boosters -- so take them with you and check yourself. The trunk is big enough for your needs for 3 children (I have 3 children so I know) -- diaper bag, stroller, groceries ..
But it will be hard to put everyone in the car and then buckle them. You need extra 5 to 7 minutes .. unless you can see the children can do it themselves. With the booster seats on the side of the car seat, the buckle is harder to get to -- so even if a child knows how to put the belt, they can't get it or at times their little fingers get squished (crying and few minutes there..).
Now the reliability issue .. We had several Hondas over a period of 14 years .. and our civic broke down (perfectly maintained by the dealer and always treated like a baby -- including cleaning, washing, waxing ..my boys are just used to of cleaning the cars every other weekend) at 106000 on the highway (The car was at the dealer for 19 point check up and all the good stuff a week ago) -- It was a nightmare with three kids (8,5,5) in the car and on the highway in the rush hour traffic. The kids had to come out of the car and helped pushed on the side -- Imagine that .. I was so nervous if someone hits them behind and they get run over by a car/truck.
Now the car is fixed couple weeks ago by the dealer, and 50% expenses were paid by the dealer for goodwill (they know us as we are regular customers -- from oil change to anything that the service suggests) -- I doubt I will have faith in Honda Civic again .. Not to mention the rental car and extra cash to get the car fixed .. We had bought the car new from the same dealership .. and recommended many friends to buy from there and they did buy it also .. But I do not think I would now be able to do that .. Breaking car is one thing .. but a well maintained car which has just gone for service (so we have peace of mind when driving with kids).. and with no warning .. just stalls and stops at the highway .. that was a nightmare.
I have many friends who have either Camry or Hybrid Camry and just love it .. I do not know how much price difference .. but you may want to look into that.
Take Care
S.