Mourning was going to be lifted for a day anyway to celebrate the Empress Marie Feodorovna's birthday. It would have been an insult to the empress to insist on maintaining mourning for her birthday. And this was the beginning of the reign of Tsar Nicholas. It would not look good for his uncles to try to overthrow him so early on.
I'm not entirely sure the uncles would have been united on that point, either. Paul and Nicholas were fairly close in age and they got along well. And Sergei was married to Alix's sister, so I doubt he would have had any objections to the tsar marrying his sister-in-law.