As legal guardians, you are entitled to the exemption for your grandchild, but only one of you can claim it. Decide who should do this; it depends on who will save more in taxes for the family. You do not apportion the exemption between you.
Increase in value of property due to market conditions. When you sell appreciated property, you pay tax on the appreciation since the date of purchase. When you donate appreciated property held long term, you may generally deduct the appreciated value.