There are a few different courses of action w/o having to replace the housing. Do a youtube search.

 

You better run in and let them show you the axle and housing and how much play there really is. Shops always want the big-money repairs. Since no housing is avail, and let's assume it's not super sloppy, tell them to put a new bearing on there, clean the mating surfaces with acetone, and roughen with 80# emery cloth. Then apply loctite red on there for now to 'glue' the bearing in. Then lower the vehicle but don't drive it till it's 'set'. You want it to 'set' with the weight on the wheel. That'll hold it and you'll never have a problem. But tell the shop you'll continue to look for a housing (fib) and have them change it when you find one (fib #2). Some shops may not want to do a bearing glue job.... So tell them it's just temporary. Like I say, it'll remain good forever probably ...or until the bearing starts to go.

Or, If you want a better adhesive, there's a product used for adhering brake lining material to brake shoes (link HERE) ...or it can be used to adhere clutch material to clutches. It's like an epoxy that turns to almost glass. Real high temp. I used it to rebuild a clutch (new material on old clutch plate) from scratch on my dad's tractor he uses for mowing a large amount of grass (3 acres??). A replacement clutch iis no longer avail. He's been using it many hrs a week for the last 4 years and it's still good. It'll never fail at this point I'm pretty confident. I did a thorough job on that. It's a great product. Scuff that outer (new) bearing with course sandpaper (and the housing) and glue it in with that. If you ever have to remove, just heat it with an acetylene torch and pull it out. I could give you some personal JB Weld success stories, but this stuff is a lot better than JB weld for your axle kind of job.

Pardon Our Interruption...

 

LocTite 620 Bearing Mount is a life and $$$ saver. Just don't let any seep into the bearing lol!

 

OK, great idea to use Loctite. I have communicated that idea to the mechanic. He doubts it will work I told him to try it temporarily while I look for a replacement differential. I pick up the vehicle today so I will soon find out and I will report back. I doubt he will prepare the inside on the housing will the sandpaper. This looks like a job that I need to supervise to make sure it is done properly.
I was under the impression that the axle needed to be removed to replace the wheel bearing but apparently not.

 

If it just spins, as in minimal slop, green Loctite 620 will 100% work. Been using it on cars and machinery for decades.

 

You have to think like you are the glue in the bearing gap here: Once he does the loctite (on a hoist) the adhesive will be mostly in the gap on the top of the bearing (where the gap will be when it's on the hoist when the weight of the axle is pulling down). Then, the gap will shift to the bottom once he lowers the vehicle and moves it out (weight on the bearing top). So hopefully some or most of the adhesive will shift around the bearing and not squeeze out when he lowers it down. Most likely it will.

Personally I wouldn't even roll it out the shop once it's adhered. But he might have to. But for sure, regardless, don't rush the job. Let the adhesive set up properly so it'll work as directed. Look up the set-up time on that and give it n+20%. Pick it up tomorrow morning or whenever the setup time is plus a little extra. Don't rush the job. You don't want to get in and drive and have the possibility of the bearing spinning or moving even a small amount till it's ready. Just like you don't walk on your deck (or floor) until well after the paint has dried.

If the adhesive doesn't work it would probably be because it wasn't done 'right' or under the ideal process, or wasn't given the necessary time to set up fully (rushed). In which case you could always redo it. The key is to fill the void around the bearing with a high-temp adhesive as possible, and let it cement in there as good as possible. Then put it back into service.