Walk away from any rescue that doesn't insist on a thorough homecheck before adoption.
When you go to meet the dogs, I'd recommend not taking yr children on hte first visit - it's too easy for heart to rule head, and you need to stay calm, focused and objective. Ask the foster carers what is known about the dog's history and background - sometimes this can be very detailed, othertimes sketchy, depending on the route through the rescue system. If you know what breed/cross they are, please make sure you have researched and thoroughly understand the breed characteristics and think you can live with them. Apologies if that sounds really obvious but often adopters don't!
Foster carers will usually give you a detailed picture of how the dog is in a home environment, and their health. So you should be updated on vax, chip, spay/neuter status, any health treatment provided or health issues known about. Behaviourally, they can advise on dog's current status WRT housetraining, being left, walking on the lead, general level of training, interactions with DC, interactions with other humans, interactions with daily life, how they travel in the car etc. Food wise, they can tell you about current diet and what dog is thriving on.
Ask if you and the foster carer can take the dog for a short walk - observe how the dog interacts with foster carer, and how it behaves on the walk. Remember you are not necessarily looking for perfect lead manners at this stage, but it's useful to see if it's reactive on the lead etc.
It's perfectly OK to say thank you at the end, and walk away - meeting the foster carer does not oblige you and if you have doubts, it's better to not proceed, than to go ahead and then ahve the adoption break down. If the first meeting goes well, then it would be good to go back with DC and have second meet to see how they and dog interact.
Good luck! 