I traveled to Hawaii with my wife but I forgot to include my Alaska Mileage plan when I reserved the tickets. I submitted my request trough Alaska retro credit website and mine went trough but when I try to enter her information and using my Alaska Mileage plan number but it wont let me. Also recently I bought some tickets for my parent and paid with Alaska credit card , can I claim miles for that travel too ?
No, you cannot. Frequent flyer programs are traditionally designed to reward the traveler, not the purchaser. They were a differentiator at a time when fares and routes were tightly regulated, and the high cost of tickets made non-business travel a rarity; most frequent flyer programs are still aimed at attracting business travelers, who fly more frequently and pay higher fares than typical leisure travelers.
There are programs that allow you to pool miles among family members, but Alaska is not one of them. The name on the ticket and the name on the Mileage Plan account must match exactly, or you will not receive credit.
Alaska does have a program which lets you transfer miles between accounts, so your wife would accrue miles on her own account, and your mother or father on her or his own account, and you could then transfer them to yours. The rate is quite high, however— $10.00 per 1,000 miles, plus a $25.00 processing fee. To transfer 25,000 miles, the barest minimum for a domestic round trip reward ticket in the U.S. (and quite a rarity these days) would cost you $275, and then you would face the additional fees and taxes on the redemption itself.