I would recommend trying a different time of day - most one year olds are knackered by 5-5.30pm - it is time for dinner and bed. I find that first thing in the morning works much better, straight after breakfast ideally so you have a window of opportunity before the first nap of the day. Little ones get very tired quickly so expect to take breaks if you are going for a longer 'lifestyle' type session. I would ask parents to bring snacks, drinks and baby wipes!
I would use your 50mm lens and no tripod although if you are new to photographing children you might find a longer lens a bit easier as they do move around pretty quickly at that age (if they are walking?)
There are tons of pictures on my blog if you want ideas - it is a really fun age - just don't expect them to sit still - but much more fun if they are running around anyway.
Unless you are really lucky it wont go according to plan, photographing children rarely does, so keep your cool. Act as if the unexpected is just what you had planned for and go with the flow. If you keep calm and relaxed then the parents will and everyone will enjoy themselves. Sounds silly but I know when I first started I used to get worried if something went a bit wrong - child fell over and hurt themselves, or turned up in a bad mood or anything like that but now I just take it all in my stride and it relaxes the parents if that makes sense.
Have fun, photographing children is the best