I think concept, price etc. will depend a lot on the area you're in. I'm in London.
The concept would definitely be popular. It's such a child heavy area that any concept that has someone else entertaining your DC for a bit is popular. We have Gymboree, Tumbletots, YMCA, Jellybeans, Twisters, Fun Factory, Action Kids etc. all within a ten minute walk and they're all full. Personally I like your concept for older children, but I wouldn't bother with a baby under 6 months and probably not under a year. I don't think a newborn baby cares about 'under the sea' tbh.
The price is OK for older ones, but again not for tiny babies. All the activities we do, babies under 6 months are free. I wouldn't pay £6 for a newborn baby to be entertained because they would get nothing from it. For older ones £6 is on the cheap side here, most are £6-£8. Gymboree (and a few others) is £10 and very popular. Most offer a sibling discount, usually along the lines of £8 for one child and then £2 each additional child. Some offer a family rate, so one child is £8 and a family (as many children as you want) is £15.
I would be more likely to come if it was 'drop-in'. It'd have to be really amazing to make me sign up for a whole term. I tend to mix the more expensive activities with the cheaper playgroups. As there are so many activities around I don't like to commit to one all the time.
I would put the refreshment slot at the end. No-one needs a refreshment after 20 minutes. It will offer more flexibility with times e.g. those that need to get home straight away can without missing any of the class. With older children it will be a nightmare to re-engage them after 15 mins of biscuits and juice. Once they're involved in the class, keep their concentration.
I much prefer Make Believe Kingdom to LaughterTots, it sounds more 'special'. Laughtertots sounds very generic. There is a baby activity thing near me called 'The hub for bubs', which I think is the worst name in the world and it's still popular so maybe the name doesn't matter too much? 
I refuse to go there on principle.
I like the website. A really fussy minor point, but in the pre-school bit, as an example, you use the word activities/activity 6 times in one paragraph, it didn't read very well iyswim. I'd also be wary about saying that the activity will vary week by week. You're asking people to sign up for a term of activities at a reasonably high price, they need to know exactly what they're getting. I would want to see a full term plan e.g.
week 1 - under the sea - fun with puppets, stories and songs
week 2 - teddy bears picnic - role play, stories and songs
week 3 - down at the farm - sticking and painting, stories and songs
I would also try and make the majority of the session consistent. Children like routine and repetitiveness. The different themes are a nice idea, but I think if they know to expect songs at the start, then an activity, then a story, then a final song it will be better than completely different each week.
I would also suggest (I know you didn't ask) changing the age groups a little bit. They're quite specific so you're ruling out anyone with more than one child really. You have a 6 month old and a 3 year old, which class would you attend? You can't take a 3 year old to a class full of newborns can you? You could maybe take the baby along to an older class, but once she is crawling/walking she'll be in the way of the bigger ones. I'd maybe do 'babies' (under 1's only, to cater to the PFB market) and then 'big kids' (babies welcome too).
If you really want to do specific age groups I'd alter the grouping a little bit. I'd probably do under 1's, 2-3 year olds and 3+. I think the ability gap between a 6 month old and an 18 month old is too big and the same between an 18 month old and a 3 year old.