My understanding is that they'll be looking for specific genetic changes in your daughter first. For example in the 1st round of tests, they'd have been looking at a range of known gene mutations/full or part chromosomsal duplications or deletions which are common in people with the symptoms your DD has. In the 2nd round of tests, they'll look for less common genetic changes.
Looking at a person's full genetic code and comparing it to 'normal' is very time consuming and expensive. So they pick and choose the bits to look at based on what they think the most likely genetic candidates are.
If they find a genetic difference, then they'll look at your and her dad's samples for only that one particular gene/bit of chromosomse to see if it was inherited or a spontaneous change.
So your partner not being her dad shouldn't affect her results.
But in either case, they'll not be looking to prove/dispove paternity with these tests. So even if they find a genetic change in your DD and then look to see if that same change is present or not in her dad, it wouldn't necessarily prove or disprove paternity. They'd need to look at a panel of different bits of genetic material ( not just one bit in her dad's sample) to look for a 50 ish percent similar result for a paternity result.
If they happen to figure out he's not her dad incidentally, eg by blood types on medical records. They're not going to say anything about it to you as a family. They'll find an excuse to talk to you alone if they feel that it's needed. Ie if they feel like the biological father could have passed down the gene mutation and he would require gentitic counselling before having more children.