I prefer rigid (no suspension) geared bikes when they are old enough. 7 is usually a little early for gears but depending on how they ride and grow, it could be the better option (our 20" bikes are geared, one even has disk brakes). Spend a little extra for a nicer bike because you can keep it for the 2 year old. Some really like single speed options (including BMX). Realize that with gears you will have hand brakes only. Most kids don't pick up shifting until they are 8-10 years old. In the end, go for the lighter weight bike all else being equal.
At 2, the other is likely too big for a bike seat. The most obvious option is a trailer. There are other options but they are shorter term or more specialized. The trailer is an add on piece that will not drive the adult bike type (in most cases). If you do not ride much I would not spend alot on the trailer (<$100). Look for a used trailer on Craigslist.
The 7 year old won't be able to keep up with you, especially if they are on a single speed. Count on riding at 5-10mph. A liesurely pace for adult riders is about 10-12mph (some even call that slow). Keep with the 7 year old and train them how to ride safely on both trails and roads.
Hi, I have five little riders from 1 -9 years old. For the 7 yo I recommend an aluminum frame singlespeed. The Raliegh is steel, has a heavy front shock and gears to complicate things and add weight; in my opinion you don't need gears to ride flat canals and basic forest trails and neighborhoods. Real BMX bikes can really save weight, but for a basic good bike I recommend one like this Trek MT 20 http://www.trekbikes.com/us/en/bikes...ages_6_9/mt20/, or similar bikes from Specialized or Gary Fisher. They also have the geared and suspension bikes with 20" wheels if you prefer that option. I actually bought my oldest a 20" Schwinn aluminum frame front suspension 7 speed a couple of years ago at a good discount through Performance. He loves it, even the gears, but he hardly ever shifts and I just think the lighter weight and simpler bike would have been the best option. Both are OK though.
For the two year old, between a rack mounted baby seat and a Burley-style trailer,I recommend a trailer. Seems like a liability, but I always feel safer with the little guy in a trailer rather than on the back of my wife's bike. As far as keeping up, we are runners too, so I usually run with a double baby jogger while my older three 6,8,9, ride bikes. It's a challenge to keep up! The rack mounted baby seat seems flimsy and makes the bike very top-heavy. It seems unstable to me. The trailer lets two ride side by side and has storage room for groceries or a swim bag! I got ours froma neighbor and I second the suggestion for buying a used one. Hope that helps.