I've done puppies and young children and torn my hair out over it. I ended up talking to a trainer about it as I really couldn't see how to make it work and she gave me the best advice ever.......
Children can't behave how we need them to in order to properly and consistently train puppies. Therefore mixing puppies and young children will always have a detrimental effect on any training the adults are doing. Children can't not react to pain and puppies will always react to a squeaking child more than an adult so keep them separate until the pup has grown up and learnt bite inhibition on adults who can be consistent with the pup and deal with the pain
.If I was in your shoes, I'd keep Daisy mostly in the kitchen (which will also help with controlling the toilet training around your baby) and let her out for short play sessions with your older child only at this point, but with her wearing a long line and the second she starts nipping, quietly remove her back to the kitchen - she will learn that nice play gives her more time but it takes a while. If Daisy is anything like my second pup Dave, you will have to do this until she is about 9-11 months or possibly longer. It seems hard at the time and you worry about the pup not bonding with the kids but based on my experience it's worked brilliantly for the following reasons:
1. Reduced the stress and excitement levels in the house
2. Contained toilet training
3. Pup couldn't eat kids toys risking big vets bills and upset kids

4. Pup couldn't attack kids and didn't get fuelled up about biting the kids because they scream and it's fun for pup - which is another reason pups target children.
5. Kids and pup learnt a calm healthy respect for each other gradually over time with short supervised play sessions that gradually increase as behaviour improves
6. Training the pup is restricted to adults so pup doesn't get confused
I could go on and on.... for me it's the BEST way to make sure the pup and kids grow a great relationship and never end up with issues with each other - a hurt child can easily react and hurt the pup which can result in the pup fearing or becoming properly aggressive towards the kids as the pup gets older and a kid can become fearful of the pup meaning they give out the wrong signals to the dog and never learn to relax with each other.
For night time toilet training, if you're not going to go down in the night, I'd leave Daisy's crate open (but still leave her confined in the kitchen) and leave some paper down away from the crate so she doesn't have to mess in her space, then quietly clear it up in the morning and continue your usual day time toilet training. If she's still messing in the night when she's about 8-9 months then you could consider closing the crate then to encourage her to hold it through the night as she'll be big enough then.
My second pup (Dave) wasn't really allowed to mingle freely with the family until he was nearly a year old as I have quite a hyper son and it was just a disaster letting them wind each other up

The pup would get freedom in the house in the evenings though when my son had gone to bed and have a good play with us, so it wasn't all bad for him. He was an extremely aggressive puppy but has grown into a really sweet family dog and he's brilliant with all children now. He's just turned 3 and I have a 1 yr old baby now also who I totally trust him with and last weekend Dave and my son who's now 7 yrs were placed 4th out of 25 in a junior dog handling competition and they absolutely adore each other
I really believe had I not kept him mostly separate to the kids in the first year, he could have turned out very differently as he really couldn't handle any sort of confrontation as a pup and would just attack - I couldn't even say 'no' to him without him freaking out and going for me

But he's learnt that no one in the family, including the kids will hurt him now and in return he's very gentle with all of us and has learnt to trust

Hang in there!!!!!