How old are the "kids?" Are they toddlers who need to be watched over every minute or young adults who can fend for themselves?
I'm thinking of your luggage. If the kids are young and one of you has to watch them while the other plays sherpa, then get a car service.
If the "kids" can manage their own bags then either the Heathrow Express or Elizabeth line to Paddington, then either a cab or the Underground (District or Circle Line) one stop to Bayswater.
Personally, I would get a quote for a car service. As stated, with four of you it might not be much more than taking public transportation and it's door to door.
BTW, if you tell us the hotel, we can give you even more precise directions.