Yup, reserving the night before is a good idea, and KL hotels in my experience are quite cheap, so it's not going to blow the budget. Or the first post about phoning them and telling them the situation is also a good one. They arrange late check-outs for people, so why not early check-ins?
I'm sure those 2.00pm check-in times are really for when the hotel is full, so they get time to clean the vacated rooms - I doubt the hotel will be full so it is worth asking. Plus, by the time you arrive and collect your luggage and get there, it will probably be more like 9-10.00am.
Good luck with it, and re the breastfeeding, get a shawl or something so it's not so obvious and sit in quiet corners if you are worried about it. If you are in hotels and restaurants, you can ask them if there is a quiet place to go to feed, and they can often be surprisingly accommodating about this.