E.M.
Ask for help with party. If family is in the area call them to help with entertaining and seating (i.e. folding chairs etc). Friends can help with entertaining and seating too. Don't be shy because people usually like to help with parties and if not they'll probably let you know. Entertain with simple comfort foods and board games, Wii, TV, cards - whatever you do on rainy days.
Eat first. Set up little area with toys for one year olds to play. Open presents at the end. If you feel you must give party favors give a ball and a book to each child. However, I don't think 1 yr olds need party favors.