Can having radiation pellets implanted in me expose my family to radioactivity?

Yes: Radioactive seeds like iodine give off radiation that decreases over time called decay. One can decrease exposure by increasing shielding, distance and decreasing the time of exposure.

Yes: Depends on the pellet type. Most likely iodine or palladium. You should have gotten instruction on who to avoid. Rules are usually for children less than 13 & pregnant women. They should stay off your lap and not sit next to you. 2 feet away is safe and it's for 6 months with iodine and 2 months for palladium. After that time there is no more rules.

Only harmless levels: If pellets are inserted, you can only leave a controlled environemnt if the dose is sufficiently low. In prostate cancer, we urge pregnant women and children to avoid the implanted person, or at least stay 5-10 feet away and limit time at closer distances to give a quick smooch.