Is there a place to store children’s booster seats?

You will have to call them and check though i think its possible and they may consider.

I don't know of a coat check...and the lockers are very small.

Check if their coat room takes them

No. There are lockers but they get taken quickly and they're only big enough for a jacket and purse

I'm pretty sure lockers are available for storage, but you'd want to contact the museum to confirm and ask how big they are.