You know, I think this is one of the hardest things that have to be sorted out as a parent. It's the one time of your life when you really don't have the time to sit down and talk it through together, so you end up doing a sort of dance around each other.
I remember when dh was trying to get dd to take a bottle (we were told better to get him to do it as she would smell the breastmilk on me) I used to try and hide upstairs but be constantly hovering on the middle step as I could hear the struggles and would try and come in to help (but would only make it worse). However, once I forced myself to stop this, it did give me a bit of breathing time to properly think out the situation. That might be what you need? It's easy to get so caught up in mothering that you don't step back enough to see the issue.
I think you've got two issues: your dp actually caring for your dd and you getting a break. It is absolutely fine for you to complain if his version of 'giving you a break' involves lights going on, dd crying etc. If you can find time, talk this through on how he could actually HELP you.
Your concerns about how your dp cares for your dd are a bit different. Try and step back a little. Is he actually harming your daughter by dangling her under a tap (for example, could it be too hot and she could get burned? or is she likely to get scratched by the tap fittings?) or has he just got a rather bizarre changing method? In which case, it's better to let him get on with it (although take a photo so you can laugh at him in future years!), step away and do something else so you don't worry about it.
Trust me, as time goes on you will really value his help with dd (and so will dd). If you can, take a deep breath now and let him learn his own techniques so as the months go by you don't find yourself doing it all. Men are such creatures of habit - if he doesn't do it now, he won't be doing it in 6 months time. If what he does now makes dd cry, don't step in and rescue him, he'll soon learn not to do it again!
It's important to remember there is no right and wrong way of parenting. I use this as a mantra every time I visit my mum!