I used a private driver, had to pay cash but got the legoland tickets off him and checked vs online price and the tickets were cheaper. We splashed out on a top luxury vehicle think the return journey was $280SGD - definitely can be done cheaper.
https://www.sgmytaxi.com/
We were picked up at our hotel at 8am and were at Legoland around 9:30am. It's not always 1.5 hours at the border.
When we went we were allowed to stay in the car to be processed, just handed all the passports to the driver and he gave them to the authorities and we were verified by waving through the window.
I believe now that has been changed and every person has to get out of every vehicle at the border. So this may add more time.
We were then picked up from Legoland at 6pm and were back by the pool at the hotel in Singapore by 7:30pm. (yes, you need to be processed at the border again..including filling out those annoying immigration cards)
It was a longish day but the kids had an absolute blast , it was one of the top highlights of the week long family trip.
As for legoland - there is a theme park and a water park. We were really lucky both were very empty on the day we went.
Water park we did from 10am to approx 12:30pm and we did plenty of stuff there, multiple rides on slides etc - but there were no queues at all.
Had a quick lunch in the themepark and covered off that whole park by closing time (again-no queues) which from memory was 5:30pm - we were allowed to shop up until 6pm and spent a fortune on lego.
If the park was remotely busy there is no way 1 day would cut it and there is enough there to justify staying overnight and doing 1 full day in each park. Or half day water and 1.5 days theme park.
I will say i went there with low expectations and it far exceeded them so my review of the place may be a touch too much on the 'glowing' side.
Kids had a blast and i guess that was the main thing, they enjoyed it way more than Universal. Ages at the time were 10,8,4