My advice; If you feel this in genuine neglect then get off of Mumsnet (sorry mumsnet) and report it to social services like any of us would report any serious concerns of neglect of any children. Of course you can do it anonymously.
If there is neglect then by reporting it now you are not only helping to protect the children involved, but also your own children who will be raised next to these (potentially) damaged step children. If there is serious neglect, it will only get worse as the children get older. You can't seriously be considering denying the children contact with their dad in his home because they have nits 
Your DP can't let the fear of no contact loom over you. Been there, done that, again, it will only get worse and where do you draw the line? Soon enough it will be the children who are old enough to vote with their feet and then what?
I am wondering (as there have been a few of these piratemum type threads recently) what it is about these men that make them so incompetent of parenting their own children. So they work long hours? Fine. So do I. So does my DD's dad. So does my husband. People have done for centuries. Then what about single parents. How do you think they manage without a live in unpaid au pair stepparent in situ?
OP, your DP is allowing you to get all upset and stressed (with a new baby) about the parenting of his children which him and his ex should be doing.
So, from a concerned bystander's point of view - report it. Then do what you should be doing in your step parent role... support the children and your husband. if you think things are wrong and you are losing respect for your husband because he is allowing his children to be neglected then quiz him on it by all means. Then support him in his actions to protect his children. Or standby while he does sweet fuck all. Or leave.
Has he done any research in to nits and treatment there of? Has he taken them to the doctors about the nails?
Is his contact court ordered? If not, can he make a doctors appointment and take them out of school to attend it? If he does it around a lunchtime he would have enough time to use the opportunity to comb their heads as a top up to what he would have already done during contact earlier in the week.
As a slight aside, my DD had nits two years ago (Year 1) and the buggers just wouldn't go away. I was mortified to have to send her to her dad's EOW and sheepishly telling him and his wife that yes, she still has nits 
Maybe ex is a neglectful bitch, maybe she isn't. Who knows. I think what everyone is saying is that you need to take a bit of a step back and have a think about who should be safeguarding these children and if there are other ways you could focus your support.
And get a new HV. That one is shit.