Can someone install a new air condition during the 3 weeks for shalom bayis reasons? Also, does one make ha-tov ve-hametiv?
It is permitted to install a new unit during the three weeks.
As you note, the berachah that one makes for the new unit is ha-tov veha-meitiv, and not shehesheyanu, and therefore the problem of making a shehecheyanu blessing does not apply. The ha-tov veha-meitiv blessing should be recited upon having the unit installed.
Although may still remain preferable to avoid “joyful purchases” in the Three Weeks (there is no technical prohibition or recommendation), shalom bayis is certainly good enought cause to waive such concerns.
Sources: See Iggros Moshe, Orach Chaim 3:80 concerning buying a new car in the Three Weeks: He writes that if one has a wife and family, so that the blessing is hatov vehameitiv, there is no prohibition involved in buying it.