Daisy, is there any chance you could do cycle monitoring? that would really help if they could check your bloods and scans throughout the cycle to establish what's going on. temp and even OPK can be misleading.
I think it's possible to ovulate during your period (but very unusual), there wont be a pregnancy as there is no time for the egg to mature and for lining to grow. it's also possible to ovulate twice in one cycle but I guess it should happen roughly at the same time otherwise you get hormonal mismatch: your yellow body of the first follicle starts producing progesterone following the release of the egg while the second follicle is still producing oestrogen does not make sense. during my first IVf I had two follicle: first was collected but the second one was not collected and it seemed to have ovulated on its own at some point after EC. hard to say when but I had a scan after I got my period and there was a yellow body on its place so it must have ovulated. (basically I had two yellow bodies one on each ovary so I guess if you ovulate twice in one cycle that's what they will see on the scan after ovulation and that's I guess the only way to confirm how many follicles ovulated. but I think this should happen at the same time more or less not several days or a week apart). though I am not an expert my observations are just based on common sense and may as well be wrong.