My husband is Persian and our daughter is learning it, but it's been tough. My husband somehow thought she'd just "get it" since she is Persian, which always puzzled me since he and I always speak in English, he used Persian only a bit with her and we lived in an Arabic-speaking country. When it became painfully obvious that it wasn't happening, he began speaking more with her in Persian and she wouldn't have anything of it. Eventually, however, she softened and would sing with him and listen to stories (waiting out the first Persian telling to get to the English translation telling, but gradually catching more and more). It helps a lot for me to be out of sight and out of mind when they get started chatting in Persian, so for a long time I'd quietly disappear if they seemed to kick into it. Now, I can be around and she'll stay (mostly) in Persian, but they love the papa-daughtalu time, too, and will go off on walks or whatever where they'll just stay comfortably in Persian or slip around in Persian, Arabic and English.
Another thing, when my husband began worrying about her not doing any Persian, he tended to get too teachy and she balked big time. He had to back off and make it fun. She loves stories of his childhood pets and adventures (which he told her he just can't explain in English) and those became his best tool to crack her resistance. He often tells these stories at bedtime and her Persian and Arabic have improved vastly since we began switching off bedtime story duties _ he tells or reads stories in Persian or Arabic on his nights (sometimes translating all or parts in English afterwards).
She's still shy with her Persian around his side of the family (whom we live near now), but sometimes forgets this in the fun of a big family dinner and uses it without thinking. Unfortunately, a thrilled auntie or uncle too often points this out making her self-conscious again, but in the past six months or so she's blossomed a lot on it, much to our relief. Her English, however, is miles ahead. My dd, by the way, is 5 1/2.
You mentioned the possibility of a Persian-speaking nanny. If that's realistic, I'd leap all over it, especially if your husband isn't really into speaking Persian with your dd. Since the nanny would be your employee, you could have a ground rule on hiring her of no English with your daughter (too bad that can't work with husbands!). They'll work out ways to communicate with simple words and gestures until your daughter picks up the language. A nanny would be with her a lot, so I'm sure it'd pay off. You asked about language resources as well... We have one 2-disc set that my dd really likes called "Shahrak Alefba." It's a man singing really cute songs teaching the alphabet (written letters and their sounds) on the first disc and singing simple kids poetry on the second. The set is a theatrical rendition of a bright, airy boys classroom and there's a muppet-type puppet along with real boys who are doing the learning/participating. My dd likes it a lot and runs to get a whiteboard and draw letters and words along with it. It's all Persian, no English on it. Unfortunately, I don't know where it would be available (a relative picked it up in Iran for dd), but you may try searching online for it or similar from bookstores in areas with large Persian populations (California?). You may find kids music discs this way, too. Also, Iranian movies are great! Often the central characters are children because of film taboos, etc., but that makes them accessible to kids and adults. Finding them probably requires finding a video store that at least has a big selection of foreign films. Good luck and I hope you (or maybe your in-laws) will be able to convince your husband to help you out with the Persian.