Well, I think it depends on how well the older dd takes direction! My dd is only 22 months, so I don't know what it's like to reason with an almost-4-yo. But I would start by sitting down and talking to her about why (in kiddie terms) you think it's important that your family try TV-free for a week--in other words, let her know that this is not a punishment and it's not arbitrary, but something you're doing FOR her.
I would also emphasize that, while you're getting the LO down for a nap, older dd gets to do "special" projects--and that you will come and join her as soon as the LO is asleep. Stress how important it is that you not be interrupted with the baby, b/c if baby doesn't nap then you and older dd don't get time together alone. Then go out of your way to find things she'll really enjoy doing and give her the "instructions" ahead of time, so she has a chance to ask questions BEFORE you're actually putting the baby to sleep. Does she like jigsaw puzzles? Crafts projects might also be nice, as they are quiet but time-consuming. A couple of thoughts:
1) Paper plate masks (cut eye holes in a couple of paper plates ahead of time); set up a table with crayons, feathers, beads, pompoms, pipe cleaners, construction paper, stickers, glue, etc. Dd's "job" is to make the one or two masks--and then when you get back, the two of you can act out stories with them. Sock puppets could work, too.
2) tape a giant piece of paper to the wall, and tell her to make a "mural" about your family; when she's done, she can tell you about it, you can add your own details, and then your dh can add stuff when he gets home.
3) sticker books! When my niece was that age, she could spend AGES peeling and sticking stickers--Barnes and Noble sells a series that allows little ones to put the stickers in different backgrounds, then unstick and move things around (there's a dollhouse one, for instance, where you can dress the dolls, arrange their furniture, set their table, etc.); Alex toys also makes sticker sets--e.g., city backgrounds that you can fill with cars and people, "pizza" backgrounds that you decorate with different toppings, etc.
4) a blank book that she can fill in with her own story (again, markers, stickers, etc.), then you can "read" it together