T.H.
Okay, this may be a dumb response, because even as I'm typing it, I'm not sure I'd do it...but here goes...I was thinking if you got a covered inflatable such as a bounce house instead of a slide thing, you could still use it if it rains couldn't you?? The only problem would be getting the kids to and from if it is raining really hard, but you probably wouldn't have much of an issue once kids were inside b/c they'd have to take their shoes off anyway.
Also, how big is your house? Could you just do something indoors? You could come up with a theme that would please both age groups and go from there...some ideas might be balloons, pizza, farm animals, etc. One year olds won't do much except run around and play with toys anyway, so there would be no need to make up games or activities for them.
My last theme idea, although this one also depends on the weather unless you have a garage, is bubbles. Both groups of kids would love bubbles! At my daughter's parties I always put out two huge rubbermaid tubs (clear and low to the ground) filled with simply Joy liquid soap and water. Fill it with household objects, anything that has a hole...strainers, slotted spoons, six pack holders, lids, string tied in a circle, etc. The holes don't even have to be round, the bubbles will always come out that way though.
Good luck!