We have a well behaved dog. We are not able to have her at home during Yom Tov/Shabbos. There is another Jewish family that would like to have her at their home for Yom Tov but there are not comfortable regarding the halachic concerns. Could you please advise? Thank you.

I'm sorry for the delay, but just read your question now. In general, anything that a Jew is not allowed to do, he cannot ask or cause another Jew to do either, for this is considered the figurative of, "You shall not put a stumbling block before the blind" (Vayikra 19, 14), i.e. causing others to stumble spiritually.