Burmese cats are cats of extremes

When they are happy they are very very happy, but when they are stressed they can become ultra stressed :( It could be that your cat is unhappy about either the pup or the kitten (or both) but I wouldn't expect this to affect her hydration levels unless she has stopped drinking ??? How much is she drinking?
the leaking of poo when she is struggling against being picked up
could be from stress,
How badly was she affected by the tummy bug? was there copious amounts of diarroeah? was it 'explosive'? etc It may have caused some internal problems which may have been missed?
Is it possible that she has a bite wound somewhere that has formed an abcess? Kitten teeth and claws are very sharp and they can be quite fierce in play ;)
Difficult to tell from a forum - you have to be there really

I had a 'rescue' cat once who became unhappy in our home, she was wild-born and needed to be an outdoors cat, as I had Burmese this wasn't possible. She became more and more antisocial and would attack our dog (who she grew up with) if there were any sudden noises (postman, car going past etc) she then progressed to pooing in odd places and 'going' for anyone who happened to walk past her and losing weight. I advertised for a new, safe outdoor home for her and she 'chose' her family (she had been dumped in my arms as a tiny kitten) after a period of settling-in she was the most sociable, relaxed, clean cat imaginable