In general Liposarcoma is a localized invasive cancer that can undergo metastasis. The usual treatment is surgical removal, thus the recommendation of the Vet for amputation. But it's disconcerting that a tumor was found on the other hip.

If the tumor on the other hip is also Liposarcoma then it has undergone metastasis and amputation won't gain much. Probably it would be a good idea to do an ultrasound to see if there are any other tumors, even if the small tumor on the other hip turns out to be benign.

If the cancer has under gone metastasis then the best chance to give Jack a few more months (possibly up to a year) of quality life is to treat with the Chemotherapy agent Doxorubicin. Concurrently the leg can be given local radiation. The idea being to get the dog into a remission, while decreasing the tumor size and discomfort to the leg. Note Jack should be placed on doxycycline prior to the first treatment to guard against a secondary infection due to tumor lysis.

If Jack has to travel down the Chemo road, then have Kate discuss with the Vet the possibility of using the Navy protocol after the Doxorubicin dose limit has been reached.

In summary: If the cancer has not spread then amputation is the best option as the Vet suggested. If the cancer has spread then Chemotherapy plus local radiation might be the best option. Tell Kate to get an ultrasound performed so they know whether it has spread or not.

Goldens seem to be prone to many cancers.