This is not a towel problem, it's an installation problem. The best thing, of course, is when you can plan ahead and put wood blocking inside the wall where you will be attaching fasteners. Since that is not possible, you need to use an appropriate wall anchor. It sounds like a light-duty fastener was used, and this pulled out of the wall so a different light-duty fastener replaced it, and this is pulling out. You would do better with some type of moly bolt or toggle bolt. Hopefully the existing fasteners have not made such large holes that they will need to be repaired first. It sounds like you are not particularly handy, so, instead of getting the contractor back who has failed to do this right twice, I am wondering if you have a friend who knows what to do...it's not that hard. Anyone who is the least bit handy should be able to put in new, proper anchors and re-mount the towel bar in under 10 minutes as long as there is no major wall damage.

On muslin, just use a tear away, remove the excess and sew on to the towel.

my first project was to embellish white linen with white cotton squiggles over the fabric randomnly and then to take the embroidered fabric and make a pair of trousers. my second project was to embroider pale green dragonflies over the shoulder and down the sleeve of a linen tunic. my third broke me to monogramming a dozen table napkins. and by the forth I was combining flower designs into bouquets and adding pithy messages and turning the pieces into bedroom pilloows with piped or ruffled edges. Now with a new machine I am into continuous borders for garments and funky buttonholes. which brother did you buy?

I think you'll want a ceiling mounted laundry rack. These are very popular among apartment dwellers in Europe. My parents in Poland have one and I think it works very well. My mom doesn't have a dryer and hangs all of her wet laundry on one of these over the bath tub. Here is a link that might be useful: Ceiling laundry rack