First, I would 100% recommend NOT adopting a dog with small children ESPECIALLY a special needs child. I don't think I could overemphasize that........1. Obviously, you are extremely unlikely to get a purebred from a shelter and a "pointer/hound mix" is not going to hunt like you want and very likely to be a nervy, anxious, and full of other undesirable behavior traits that you get when you mix breeds 2) If you luck out and find a purebred hunting breed or go through a hunting breed rescue, you still have NO CLUE how, or IF, they were socialized and to me that is an unacceptable starting point for a dog that will be mingling with my children.
My first dog was a GSP that we got from the shelter. I will tell you right now, I went the shelter route because I was cheap. It was stupid, I admit that. However, I was looking for a Lab and knew nothing of bird dogs but wanted to get into Pheasant hunting since I had recently moved to Iowa. It just so happened that they had a BEAUTIFUL 7 year old Shorthair. I immediately took him. The story was he was a serial escape artist/ wanderer and the previous owners were tired of bonding him out of puppy jail. He was a WONDERFUL dog for my wife and I, other adults, and older kids (3-5years old and up). However, he would get into nasty fights with ANY male dog he encountered....so no more dog parks....Additionally, he did NOT like little little kids, i.e. toddlers. 3 years old and older was not problem whatsoever but crawling babies and wobbling toddlers would make him growl.....it wasn't a deal breaker because it was easy enough to crate him in another room every once in a while when family with small kids came over and like I said, he loved playing with older kids......
Then we had our own baby.....We though it would be okay if he grew up with the baby from infancy, he would be used to them. That was the case for the SECOND GSP we had gotten in the meantime (we got her as a puppy from a breeder), but for him, nothing changed. He always growled and jumped away from the crawling baby. We had to be on the floor with the baby to ensure the baby left him alone or otherwise we had to kennel the dog. Well, one day we were playing with the baby and the dog just crossed the room towards us while we weren't looking, sniffed my son, and I turned around just in time to see my son reach for him and get snapped. There was no broken skin but it was clear that there was no more 'trying to make it work'. As much as we loved the dog, because he really was a great dog in every other circumstance, we had to give him away......
I will never adopt another dog while we have small kids because you just don't know what the previous owner did or didn't do to work with them. Our second dog that I worked with from a puppy is fantastic. She is the most tolerant and accommodating dog. I spend more effort keeping the babies from harassing her than the other way around. She is extremely gentle with them. She adjusts her roughness of play between my 4 year old and our 1 year old. She plays tug of war with the four year old but lets the baby take the toy right from her mouth and then she just plays fetch with him even though he can only throw it about 3 feet, and when she wants to keep the toy, she just walks away from him to her kennel and we teach the kids to respect that. When we hunt, she is ON IT. She hunts hard and finds birds. When I shoot them, she brings them back. She has tracked cripples hundreds of yards in the opposite direction that I thought the bird would go and I have to eat my words when she come back 10 minutes later with a very much alive rooster in her mouth. I try to drag her to the left where I think the birds are hiding and she insists on going right.....and of course slams on point a minute later....eventually I will learn to trust her. We haven't done any high level training, multiple blind retrieves, etc, but she is a great house dog and great hunting dog for my needs..
All of that said, I'm going to disagree with a lot of people here and say that it aint actually that hard. The potty training will 100% be the most burdensome part because you have to get up and let the dog out every two hours, or your wife does when you are gone, but it's only a couple months until they *mostly* have it. After my experiences, that is a small price to pay to have a substantially higher confidence that your dog will be safe with YOUR kids (toddlers, special needs, etc.), not just the trainer's 10-13 year old children. Besides potty training, the obedience training is just 10-15 minutes a day of basic commands, reinforced with good habits throughout the day. Don't let them jump on you, don't let them counter surf, make them wait at the door to be released, etc. It's not really like it's a rigid training schedule that your wife will be burdened by when you're gone, it's just correcting undesirable behavior when it comes up. It's not THAT hard. If she takes an active role in the regimented training while you are gone, it'll go faster. If not, it wont. That's fine. As long as she isn't actively encouraging it to eat garbage and crap on the floor, She isn't going to UNdo anything.
The bird dog training, to just average hunting ability for the average hunter, can be accomplished by an hour or two a week in the summer and then a bunch of wild bird contacts either during the summer or during your first season. The more training you do, the better he'll be. But it's in his DNA so if you just want him to find birds, point/flush, and bring them back after the shot, It's not terribly hard. You don't NEED him to be working at field trial or hunt test levels to kill birds and have fun. So much of this stuff can be done with your family present, too. My dog's puppy stage was before we had kids but just the other day I was out planting 8 pigeons for training with my 1.5 year old on my back and my 4 year old pulling the rip cord on the bird launchers. The four year old was shouting "One..Two..Three...BELLY FLOP!!!" as he lunched them and I dusted them lol.We had a ton of fun. It's all he talks about, going "pigeon hunting" with dad. My 1.5 year old now sees our homing pigeons fly around the yard and goes "Daddy! Bird shoot! Bird shoot!" and makes pew pew noises. As for time efficient exercise, get a dog roading bike attachment. Dog gets to run and you don't have to. A 1.5 mile jaunt takes me 10 minutes....I just wake up 15 minutes earlier for work every day than I otherwise would and then my wife doesn't have to worry about it. Very little effort, very little burden on the family. Days off or after work, 2x a week, we do a 6.5 mile bike ride with the dog...it only takes 40 minutes...and the kids get to ride along in the kiddie seat, too. I'd go for bike rides whether I had a dog or not, so I really don't feel like it's a burden. If anything, the dog is a motivator to go do activities you should do anyway. A dog becomes just a normal part of the family. You figure it out. Millions of people have figured it out. The difference is, During the fall I get to chase birds with my dog and they don't.
As a last note, I will say, get a mellow breed. Maybe a Britt or some lines of setters. Talk to the breeder. You want a house dog that can find birds, not field trial dog. GSPs can be fine house dogs, too. However, I won't be getting another one because the hair is ridiculous. I often see it just floating in the air in our house. It gets on all the fabric and embeds itself in the fibers and is impossible to clean. It's like glitter.