I would like to know if I’m allowed to go on a one day vacation just to rest
Up me and my wife since my father passed away 3 weeks ago and has been very sick for a while.
Yes, this type of trip is permitted.
See Shulchan Aruch Y:D 389:25, the Aruch Hashulchan [seif 33] explains that only travelling with large groups which makes a pronounced festive atmosphere should be avoided during this time. A personal trip to recuperate is permitted.