Have snacks as already mentioned, but be sure to find out if there are allergies or special requirements. Kids with peanut allergies can not even be around places where peanut butter sandwiches have been prepared for instance. So you may have to super clean or keep kids out of the kitchen or whatever, as an example.
Spare diapers or a place and supplies for changes and disposal should be accessible and handy. Some people don't feel comfortable using another person's changing area, or leaving "care packages" in their garbage can or diaper genie, so have some clean supplies or a space set aside in case she has reservations. Just offer but don't insist. She may come prepared and have no qualms about changing out in the open.
Find out what type of games the guest likes and have them handy and ready to roll. Have a variety of activities ready in fact, so if they get bored, you can keep the good times rolling.
Find out if naps are needed and what time and plan to wrap things up accordingly.
If mom is staying have snacks and a comfy place set up where you can chat AND keep an eye on the kids.
If you have a good time and want to encourage the relationship after the playdate, follow up with an e-mail confirming that your child and you enjoyed the visit and that you hope to visit with them again in the near future. No need to thank them for coming...just give them confirmation that it was an enjoyable visit so they know they're welcome to reciprocate the playdate.