Muscovy duck egg hatching

[kgold]

I have a Muscovy pair, and she 2 laid eggs around May 27th and has been great about sitting on them. As of today it has been about 37 days. I went out to the coop to check on m birds this morning, and one of the eggs had been cracked, with no baby in sight. I found the other egg cold, underneath the nesting box. I picked it up assuming it must not be alive anymore, and felt it moving. I laid it on he counter and it started to move side to side. I honestly know almost nothing about hatching eggs. I don't have an incubator, and my duck refuses to sit on it. I am currently using a heat lamp with a wet rag and an egg thermometer. Does anyone have any advice for me? Thanks!