M.C.
This is a question that is dear to my heart! I have raised 6 children - the youngest is almost 9- and have 6 grandchildren as well. No, our children were not perfectly quiet but they learned very young that there were certain expectations at church or in public gatherings, and overall did very well. Here are some ideas that worked for us. And we had children from fairly passive to highly energetic - they can all learn!
First, we started from the time they were born to include them in our daily family devotions. They were expected to sit in one spot for the duration, whether it was on a lap or on the couch or floor. They were allowed to talk - family devotions was for them, after all! - but had to speak softly, and not while we were reading the Bible story, or while a parent was talking. We also started teaching them how to whisper at a young age - that can save some embarrassment when some has to "go pee" in church!
We also held them on our laps at church till they were a bit older. This allows the parent to feel the wiggles coming. Usually a light squeeze when they start to squirm, then release when they hold still - they soon learn that sitting still was far more comfortable! If they did start to fight the encircling arm or start to cry, we'd try a soft "hush" in their ear - if they carried on after that, we immediately removed them to the foyer or ladies/mens room. The activities out of the sanctuary were never "fun" - no playing, no talking, just a firm - "Crying in church is a no-no.You must sit still. Now we'll go back and try again." For our more strong-willed ones, it could take up to 3 or 4 trips out with sometimes needing a swat to get them to "hear" us.
We never used nursery facilities (except for nursing baby or changing diapers) or children's church as we felt that was simply teaching them that you go to church to play. Eventually they have to sit in church and we found families who used the child-minding services ended up with 5-7 year olds with no clue as to what to do in a church service. By the time ours were 3 or 4, some younger, they could sit through an entire service, sing along during worship time, and then stay completely quiet with only a pad of paper and pencil.
A couple of quiet toys for the smallest children - up to a year and a few months, but after that they should be content just relaxing on a parent's lap. I woule often stroke them, or use my fingers and quirky knuckles (I can wiggle my knuckles in weird ways that fascinates children - they keep trying to catch the knuckle!) to keep them entertained.
Now I know this is sounding like its all easy and my children were angels - not so! It takes a LOT of work, energy, and most of all consistency to get the results you want! And if you haven't started from birth at home, you'll have some catch up to do. A 7 year old is old enough that you can have a conversation before the service - this is what we're going to do, this is what I expect, and this is what will happen if you don't do well. Even the 4 year olds, can learn from that chat. The littlest one will be a challenge, but if you are consistent and practice at home, you'll be surprised at how quickly they learn. I would definitely encourage having a short devotional at home every day - call it playing church and say we're going to practice for real church. It's also very important that if one is misbehaving and you need to take them out of the sanctuary, that it is never a reward - it must be WORSE to go out than to stay in and sit still or they'll act up just to go out.
As for switching to the new church - if you feel that's where your family will receive the most benefit, just do it, work on the behaviour and don't worry about the looks you get. Our youngest is a special needs child - I can't tell you how many times he'd have total meltdowns for no apparent reason and people would look at us as though we had pinched him or something! You do what's best for YOUR child and let everyone else deal with themselves. If someone says anything, just say, "Thank you for mentioning that. We're really working hard to train them properly and would appreciate your prayers."
I would also suggest that while you're in the training process, you try to sit in the back rows where you'll disturb fewer people, and it will be easier to slip out if necessary. For awhile you may not get a lot out of the sermon yourselves but as you consistently and lovingly train your children, that will change. Not only will you get more out of the service, but your children will start to learn from the sermons at a young age.
Most of what I've said is not popular with young parents. Trust me, your children will be much happier for learning this discipline!