Yellow tangs can be wrasse holes esp. With other tangs and similarly shaped fish. I have had my yellow tang for about 5-6 yrs and I have seen her b extremely aggressive to new additions and has even been the cause of . A few deaths.
With that being said I have found a few tricks to sneak a new fish in.
1) add new fish after lights out in complete darkness, at night the fish kinda sorta sleep and its much easier to slip a new fish in, I have also gone as far as leaving the lights off for a few days until they start to acclimated to each other.
2) a full fish is a happy fish. I normally feed before adding a new fish and with tangs if u regularly feed them seaweed, or nori it drastically reduces aggression.
3) another good trick is to rearrange your rock before adding a new fish. Fish become territorial of their space and by rearranging your rockscape you eliminate the territory that the fish has claimed.
I have had the best luck by feeding the fish, then before lights out rearranging the rockwork, and sneaking the new fish under the cover of darkness. And in the case of adding another tang I will normally leave the lights off for 2 days, and it has definitely reduced aggression in the existing fish and stress on the new addition.
I guess I should have started out by asking what size tank you have. Tangs (as you may know) require large tanks to do well, and if they are crammed in too small of a tank they will normally cause all types of problems.
Also I noticed you said you were having an algae problem I hope that was not the reason for buying the tang and lm blenny because if it's anything g other than a very small outbreak they will not help you.
If you are having algae problems the best/only way to get rid of it is to find the reason why you are hAving the outbreak in the 1stplace. Some common reasons would be high phosphates, high nutrient levels, or even old bulbs. The only way to truly eradicate a nuisance algae is to find the cause and kill it at its source.