we'd prefer for our partner to host or we will potentially cover the cost of hotels. Our current plan involves our child being at our home while we're on dates (either with one of us watching them or a babysitter at our home), so we'd rather not bring that around them currently.

So again, this is great for you and crappy for him. Usually the men you're matching with will have no problem hosting, but it's weird for a guy to never be able to host. You also say "potentially" cover hotels like that'll be a problem, do you realize that either way he's going to have to pay for dates assuming he gets any?

Also, since you'll be going on ten times as many dates your last rule basically makes him your babysitter.