I know this question is a bit old, but since I came across this as a prominent Google hit when searching for help on the same thing, I figured I'd post a more complete answer for anybody else who comes along..
For context, the line in question appears to be from the "よつばと!" ("Yotsuba&!") manga, in the first volume, page 8 (3rd panel). Yotsuba and her father are driving in the car, and the full exchange is:
The portion in question at the end breaks down to:
- 俺 ("I"/"me") + の (posessive particle) + 分 ("part") ==> "my part"
- も (particle) ==> "also"
- よつば ("Yotsuba" (name)) + が (identifier/subject particle) ==> "you" (subject)
- ふって (te-form of 振る: "to wave") + くれ (idiomatic form of 呉れる: "to do for someone") ==> "wave for me"
As you noted, くれ is related to 下さい; however, they are not really the same. ください is a special conjugation of くださる, which itself is the honorific form of くれる. くれ is a special idiomatic form of the (non-honorific) くれる, so the basic action (to do something for someone) is the same, but the politeness implications are very different. くれ is a (fairly masculine and informal) direct command, as opposed to a polite (honorific) request.
For more information on くれ and friends, you can read through Tae Kim's excellent page on making requests
As a side-note, I had originally read "とーちゃん手がはなせないからな" as "Daddy's hands can't speak right now" (which seemed a little poetic/idiomatic, but actually could make some sense when taking about waving to people, so I didn't think too much about it), but @Mauro pointed out that the verb "がはなせない" (はなす) there is probably not 話す (to say / to speak) but is actually 放す (to release / to let go) instead, which would make it more like "Daddy's hands can't let go (of the wheel) right now", which does make a bit more sense in context.
So in summary, the translation of the full exchange comes out to something like:
Yotsuba: The lady waved! Daddy, you wave too!
Father: Daddy's hands can't let go right now. You do my part of the waving too.