Go bigger. Wolves are way bigger than coyotes. I shot a big coyote last winter right behind its front shoulder with a 22-250. It dropped and then ran. Took two more 50g Vmaxes to kill it. Not enough penatration. I would go with something more suited for deer. If you use your deer/moose rifle your getting practice with the same gun.
IMHO, your problem there had absolutely nothing to do with your 22-250 and everything to do with bullet choice, Namely the 50 grain V-max's and speed. They are in my opinion one of the poorest bullet choices for coyote there is in the 22-250 or Swift. Great for blowing up groundhogs and crows.
Coyote's are damn tough.
I like somewhat frangible bullets but at the speeds of the 22-250 or swift They are far to frangible for my liking.
When i still had some decent health and could get out on a regular basis I tried them here in N.B. for a couple of years.
Not sure what you mean by a big coyote as it varies from region to region and i don't know where you are.
The coyotes here and in N.S. and Maine can run a bit on the large side.
The V-max's made for some very instantaneous kills....Sometimes.
Just as often though i found they splashed on impact. Even given perfect shot placement I had more runners and spinners with them then any other bullet i ever tried for coyote.
I much prefer the Nosler ballistic tips and found them to be much more consistent for putting them down on the spot.They seem to be a bit of a tougher bullet to me. I have rarely ever had a runner with them. Usually DRT.
I also had great luck on Coyotes with the Hornady 52 grain HPBT Match (yeah i know it's a match bullet but it works great on coyote's)and the Sierra 55 grain Gameking.
I know three other guys here that have tried the V-max's in 22-250 and the Swift for coyote and i don't believe any of them use them now. Two switched to NBT's and i think the third did as well.
Just my take on it. I am sure others will have different opinions.
As far as Wolves go.
I have never shot a wolf so i will have to leave that up to the guys with actual in the field experience with them.