Honestly...probably.
I can't speak for bigger rescues, but for my much smaller (breed specific) one, we prioritise those who have either breed experience or gun dog experience. It's not to say that those without wouldn't make competent owners...but the problem is we get so many with good breed experience (including handling behavioural issues) that we automatically gravitate toward them because we know the dog will be going to a home that really understand the breeds needs. Better a safe pair of hands that knows what it's doing - even with a 'stable' dog - than someone who is still learning the ropes, in our experience. We know too many rescues that re-home dogs to people and then the dog bounces back a few months later in an even worse state than before because they picked the wrong person.
And children would factor into our decision. In part because so many older children aren't dog savvy (despite what their parents think/claim) and in part because so many of our dogs, in particular, have bite histories.
The adoption market for dogs that are suitable for living with children and have no behavioural issues is so oversaturated. Everyone wants the perfect, child-friendly, dog...which I totally get. But it means that realistically, unless you have something really special to offer, you're against really stiff competition.
We had a girl a few months ago with some quite serious 'issues' (SA, resource guarding that resulted in a bite history on a child). She had 40 applications in a week. And that was an 'elderly' dog who couldn't live with children or cats and needed someone home 24/7. Our 'easy' dogs get 100+ applications. You have to be pretty special to stand-out.
My mum adopted through Spaniel Aid a few years ago. On paper she was a perfect applicant; retired, fit and active, no children living with her (although visiting grandchildren), large secure garden, experience of gun dogs and behavioural issues, no holidays outside the UK, stable finances etc. It still took her about half a dozen applications to get a dog - and even then the dog was one no one else really wanted...
That's not to say give up. Two applications really isn't that much. I've seen the same email crop up dozens of times on requests to adopt before...
Oh, and if you go to a 'big rescue' please do bare in mind most of their dogs are not properly 'home' tested and have instead been assessed inside the rescue, not in a functioning home, based off the prior owners information. Very often, prior owners lie, or the rescue lies, and they end up re-homing dogs completely unsuitable to the family. We've had a few instances in DogHouse recently of 'placid' dogs (Greyhounds, I believe) who have turned out to have quite serious guarding issues that the 'rescue' allegedly knew nothing about...
Better to go to a rescue that have dogs in foster and so the dogs are properly assessed.