So options are
Arrive in KL at 4pm, get out the airport drive to city get there maybe around 5.30ish stay overnight. (about £20 + car more for a hotel car)
If you decided to stay in KL say Traders, it would take about 50-60 mins to get to the airport, (its about 56 kms from the city dependant on traffic) your flight is 9.50 so check in 3 hours before, so looking at 7am, so you would have to leave for the airport about
6am.
You can also get the train the KLIA express to KL Sentral from the airport which is quicker but you would then have to get to your hotel (and all your luggage) by taxi from the station but more convenient to get a taxi. But there are hotels around the station but you will still have to get to say the Towers etc from there. Hilton/Le Meridian and the like are in the area.
There are trains running up until 11pm to get you back to the airport hotel if you decide to stay there and the Sama Sama hotel (with others) is right next to the hotel (landside). The golf buggy will take you back forth to the airport.
Suppose it depends as well on how tired you are after your incoming flight, you may just want to crash at the airport have dinner use the pool/spa etc. Travelling with your DD she may be shattered (or not!!!) and of course the additional cost and your budget for accommodation both in KL and the airport.
If you need any more in info just shout, I lived in KL so know the city.