I used one years ago when my kids were small, and more recently as my nephew is now at the trailer-riding age. I like trailers - very stable, lots of room for the kid and his/her toys. The child is protected by metal all around, and even if you fall over, the trailer won't. I've also tried child seats on the bike, and that puts weight high up when it tends to unbalance you and where the child can pull your hair while your ride.
As far as the helmet, maybe you could try it in the house briefly until she gets used to it.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72