Who do I send thank you's to after the funeral?

Respond to all of the above, and hopefully you had a guest book for sign in at the service. We used this for the first group of cards, and then went over all the other "gifts" and memorials, and if we didn't already acknowledge those people, we sent those cards out last, so we could include some special notes and remarks in each.

See Emily Post : Handwritten sympathy notes, flowers, Mass cards, contributions to charities, and acts of kindness should always be acknowledged (by the recipient, if possible). . Preprinted cards with no personal message, emailed notes of condolence, online sympathy notes, and visits to the funeral home or the service don't need to be acknowledged in writing. Letters of thanks are customarily written to pallbearers, honorary pallbearers, ushers, eulogists, and readers. (emilypost)
For the flowers, I would reply to the person who actually had them sent and paid for them, not all the names listed.

So sorry to hear about your Aunt. My heartfelt sympathy.

When my boss' wife had passed away this past summer, he included not only those who had sent flowers, but also to everyone who signed the guest register at the funeral home.... and to those who had sent him cards afterwards. That was a lot of thank you cards, so my boss got boxes of sympathy thank you cards from Hallmark and inside each card all he wrote was "Love, Bob".

I think it would be appropriate to send a thank-you to each person listed. I agree if it was the Aunt and children, then I would just send to the Aunt while including the children's names. If you are particularly close to the Aunt's children, I would send each a note. This is how we do it in my family! Sorry for your loss.