Just done it with 3 sprogs in from the west – Paddington, tube round to South Kensington .. as long as you don’t go in rush hour it’s fine.
Youngest in stroller (a few stairs to carry up between you mind), middle one in backpack eldest (5) was walking and being directed. They loved the journey as much as the museum.
Ask at the station for a group ticket – we were told about this by the conductor, it was cheaper than 2 adults plus one child with a railcard.. though it depends on the age of your children ofc.
I wouldn’t consider driving there, I had to work around the corner and parking was the most stressful part of the job.. couldn’t get a server under my arm on the train you see.
Oh, and keep an eye on them – middle son (2 going on 3) got proper parent panicking lost. Twice. He was fine, Mother less so.