>>2859742I don't think 45lbs is too much for a good rack, I know that mounted correctly the cheapo sunlites will do 40-50lbs without an issue. That said I think your issue is going to be density. That's just a lot of weight in a small size and unless your frame is set up for it it's going to be fairly high up. Not impossible though.
Weight is usually easier to carry on the front and that's how you will see a lot of big cargo bikes and stuff like the cargo forks set up. Trailer would also be a good idea since the weight will be much lower. Even if you found one for kids/dogs 45lbs is well within their official weight limits. I think for your purposes if not doing anything else, get a tupperware bin or similar, a couple of bolts and fender washers and attach a tub directly to the rack. That will keep the bag from getting shredded by straps or whatever. But I would be very cautious about turns and hills with that weight over the back wheel.
I am also going through similar not out of the same need but financial. I have the municipal dump that offers a free scrap yard, free mulch, and free soil if I can get to it just about a mile away. I hope acquire a bike trailer so I can get those yard supplies for free, even it's one or two containers a day. I work from home so it would be trivial to have the bike ready to rock over lunch, bounce over with a shovel, and dump it where it needs to be in the yard.