use Multisignature Application in 1-of-2 method..
This is just as good as giving the other person your private key right now.
Well, look at the responsibility of involved people in both solutions. in multisignature you could engage your attorney in the process and he/she never could spend your money with his/her secondary account without your permission on contract. if you give the other person your only private key, you will lose the advantages of non-repudiation that comes with asymmetric encryption.
I think you are thinking of 2-of-2 multisig, not 1-of-2.
1-of-2 means that either of the keys can unlock the funds.
1-of-n multisig transactions are equivalent to sharing your private key with n people, as anyone can spend it.
2-of-2 multisig wouldn't work here though, unless you want to not be able to spend your coins without your attorney's permission.
No, no. this should be 1-of-2. the 2-of-2 doesn't work here. we exactly need either of the keys unlock the funds. therefore we could track abuses.
When Alice is alive uses her primary account for transactions normally. but she also creates a secondary account linked (with OR logic gate) to her primary account, and gives its security values to her attorney/trusted_person with permission to use the keys of the secondary account when she is dead. if she share her primary account with others, she can't track any abuse of her account, but with 1-of-2, you could simply track the sign of your funds to see which sign get used for a particular transaction.
If the server gets compromised or the software fails for some other reason, a regular transaction would cause the coins to move prematurely. With a timelocked transaction you have the added security of the Bitcoin blockchain. 
