OK here's a couple of things to check out.
Watch the heat with a 20 month old.
The malls all have great soft play areas. Dubai does this sort of thing so much better than the UK. Even the small malls have huge kids play facilities and as they are all air conditioned it is a good place to take a toddler.
The best one is probably in Mall of the Emirates called Magic Planet. Lots of soft play and a couple of merry go round type things.
Also check out www.childrencity.ae This is a fab place and has loads of activities for kids of all ages.
There is not much for a 20 month old at Wild Wadi so you may be better going in on a sundowner pass after 6pm - that way it'll be cooler and cheaper so you wont feel done out if you only stay an hour.
There is a kids fun fair at the front entrance to a place called Safa Park. This is on the corner of Al Wasl Road and Al Sadiqua Street. Don't expect massive roller coasters or anything like that - it's mostly for small kids.
Make sure you take or hire a buggy, then you and Mrs amanbhullar can mooch around in the malls in the evenings after the we'an is slumbering peacefully in the buugy. Food is very cheap in the malls and it'll save Mrs AB slaving over a hot stove.