Hi awkwardas78I this is a terrible situation and I am so sorry for it. I think you have had some good advice here and in your shoes I would probably:
Not try and involve my dh too much in all this, he may not be able to see it from you or your dd's side and his grief will be too overwhelming.
Your daughter should not be made to kiss or hug him, however ill he is, my kids hate hugging and kissing any relatives and simply won't do it, the relative makes it worse by trying to talk the kids round, it is all very uncomfortable and so we make sure our goodbyes are very quick!
Persuade your dd that it is important to be polite and say good bye nicely before departing (I must admit I woudl even try some bribery, a nice goodbye and a wave from the doorway get a comic book!
Make some things for your FIL while at home, cards etc with photos (as others have said) so when you arrive there will be things to talk to him about and show him.... Personally I would go to town on this, made a really big card with a big photo of dd on it. That way he has evidence she cares, even if this isn't enough for him, others will see it and may even comment on it 'Wow granddad what a lovely card from 781 granddaughter.
Lastly as others have said, she should not be made to come to the phone and the best excuse is she is asleep, because three year olds sleep a lot!
I hope things will be ok. My nephew was about 4 when his granddad died. He was sad but he got over it quite quickly. I would feel part of 'managing' this situation is wanting to retain some happy memories for your dd of her granddad.
Don't forge your dh in this situation, he will be going through hell and will need you a lot! You poor thing, everyone will need you. Make sure you have some support for yourself, friends you can call up and chat to, people who may be able to look after dd so you can support others in the family and someone who can come round and drink wine or coffee with you and talk about something else with you! Bless you.