I have family members as well who just don't understand that putting bleach in the pool is not only safe, but a pretty good way to chlorinate the pool in general. So I feel your pain on that one. I think long term, a good solution to your problem will be a salt water generator.
You say "liquid shock". I hope by that you mean regular bleach? Often times, products have fancy terms on them that are down right shams to get you to spend more money. Just yesterday I was out and needed to pick up some more liquid chlorine. I normally use the walmart pool chlorinating liquid. It's 3.50 or so a gallon but it's 10% vs the 6% bleach in the cleaning section for $2.60 a gallon and using the 10% amounts to less plastic bottles to throw away. Anyway, the walmart I was at didn't have any and I wasn't paying $2.60 for a gallon of 6%. Then I went to the local dollar store and looked at their bleach.
They had "Top Job" bleach in a 3qt bottle for $1 but the reviews were terrible. Supposedly very low % of chlorine. I looked at the unscented regular cleaning bleach and they had "cleaning" bleach for $2.20 a gallon (at 6%) and they had "concentrated" bleach for $2.75 a gallon (at 6%). The chemical makeup and dilution instructions for both bottles was exactly the same. Your getting ripped off 55 cents a gallon because they printed the word "concentrated" on that bottled. So yea, just use regular ole bleach if you didn't.
The algae 60 won't hurt. If you want to dump it in, go ahead.