Check with your local building code folks. Most would say yes to the laundry tub but some would say no to a laundry in a bathroom.

YMMV

One other thought--you said old clawfoot tub. How old is the house, where is the bathroom located relative to supporting walls...where I'm going is---are you sure the floor is engineered sufficiently to add a washer? (Yes, there was a tub there. Tubs are dead loads; washers are dynamic loads.)

thanks ci_lantro! It's a samsung top loader, high efficiency that uses 10-4 gallons per load. The house was built in 1992. The original issue I thought I was going to come across is whether the 1.5inch pipes would drain the water, that's why I thought the laundry sink could fix that because it could hold the water and let it drain at it's own pace. I don't mind the laundry sink being there, I'm looking for the cheapest option.

Someone also mentioned to me that a utility sink needs a trap above the floor, and because the bath drain has a trap under the floor, they would have to open up our floors anyway. Is that true? I thought I could just attach a laundry sink to where the old bath drained and problem solved! But I guess it's more complicated than that. Also, I don't know what the issue is with the vent? Wouldnt' the utility sink use the existing vent that the bathrub pipes used? As you can probably tell, I am very confused and don't know what I'm doing! I just thought there would be an inexpensive way to do this without completely ripping up all our living spaces and spending 4-5k on this. :(

sorry, i meant to say 10-14 gallons per load. The laundry sink we were looking at can hold 18 gallons.

You will need to check with your town's or county's local code inspectors but, in my town of many old houses, the code inspectors read the codes:

(a) to allow draining a washing machine into a laundry-sink with a 1½-inch drain;

(b) to only bar use of an existing below-floor P-trap when the vertical distance is more than 24-inches between the bottoms of the utility-laundry sink and trap (that is do-able with some laundry sinks); and

(c) to grandfather in the 1½" pipe because you are actually going to a lesser new use of 10 to 14 gallon drain-loads from the new sink as opposed to 40 to 50 gallon (or larger) from the claw-foot tub. (FYI -- The current 2"-diameter requirement for washing machine standpipes came about when some washing machine manufacturers added speedier drain pumps that pushed water faster than could be handled by a 1½" diameter standpipe. The code-recognized solution of draining to a laundry sink solves the problem by serving as a holding tank from which water will flow out only at the speed that the 1½" line can handle.)

Now, you might well choose to do more than the laundry sink solution for all the reasons that ci-liantro mentioned. But if you've already taken out the tub, and need to do something pronto and the budget is tight for the time being, and you don't want to rip up your living space now with a big project, I'd check with the code inspectors and maybe run this by another contractor.