At a bar mitzvah, can the Kohanim be asked to leave in order to free up more aliyahs for family members?

Shalom, Thank you for your question. The Shulchan Aruch (Orach Haim, 135, 3) writes that a Cohen is called up first to the Torah reading. The Mishna Brurah (ibid 9) explains that apart from the Torah command to give honor to a Cohen by calling him up first (which the Cohen could perhaps forgo if he chose to), there is an additional decree for the sake of peace, to always call the Cohen up first in order to prevent any arguments. Based on this ruling it is not in the power of the Cohen to give up his privilege to the first Aiyah, and he must be called up first. However, there is the possibility that you raised, of the Cohen stepping out of the synagogue before the first call up, and as such there would be no problem in calling up someone else in his place. This option is discussed widely by the halachic authorities. Though some opinions do strongly reject this option, the majority opinion is that is may be used occasionally when there is a pressing need. (See Piskay Tshuvot, 135, 9). So, in your case, where there is to ba a Bar Mitzvah, and (I assume) several important guests who each need to get an Aliyah, you could request that the Cohen step out for a moment or two while they call a Yisrael up for the first Aliyah. Mazal Tov on the Bar Mitzvah!