My husband has had treatment for varicose veins. His treatment was laser and injections and full recovery takes about a year.

Yes I have some varico veins but they don’t bother me. Varicose veins are generally benign. The cause of this condition is not known.
For many people, there are no symptoms and varicose veins are simply a cosmetic concern. In some cases, they cause aching pain and discomfort or signal an underlying circulatory problem.
Treatment involves compression stockings, exercise or procedures to close or remove the veins.
Different treatments are available for more-severe varicose veins
Sclerotherapy. …
Foam sclerotherapy of large veins. …
Laser treatment. …
Catheter-assisted procedures using radiofrequency or laser energy. …
High ligation and vein stripping. …
Ambulatory phlebectomy (fluh-BEK-tuh-me). …
Endoscopic vein surgery.

My family has a history of this and we have never really done anything to get rid of them

Ask your GP for a referral to see a vascular surgeon. They can advise on suitable options which include sclerosing injections, laser treatment and vein stripping done under general anaesthetic.

My partner used a product called Vein Away. He only had mild varicose veins tho and this worked for him

The procedure is called vein stripping. It sounds awful and if you google it you can read good explanations. It is done under a general anaesthetic.

what was the procedure/??

I have a friend that her varicose veins treated and it relieved her pain. The process sounded unpleasant but she was so happy to get it done.

I have not had it done myself but it does work and I can’t remember how long it takes to recover.