I think this is so personal and also highly dependent on one's lifestyle as well as climate. And also how often one doesn't mind doing laundry! I don't like to do my laundry any more often than once a week, so for example I would want to have at least seven pairs of underwear.
If my kids were younger and I was still a SAHM, this is what I would consider "enough" - if I had to pare my closet down to the bare minimum:
5 coats: denim jacket, leather jacket, rain coat, knee length wool coat, puffer coat
7 jeans: 1 straight, 1 skinny, 2 bootcut (one for heels one for flats), 1 white denim, 2 pairs clamdiggers ... yes that's a lot of jeans but you probably live in them. I say 2 clams because last summer I only had one, and I wished I had a second pair.
2 skirts: 1 denim skirt and one floral cotton skirt (you may want more than this if you live in skirts and prefer them to jeans)
3 dresses: 1 casual cotton summer dress, one dressier dress, 1 sweater dress
6 cardigans: 3 lightweight cotton ones and 3 winterweight wool ones
6 blazers: 3 for spring/summer; 3 for fall/winter (you may be able to get by with a lot less than this if you prefer cardis for your lifestyle)
7 machine-washable knit tops, one for every day of the week; what gets tricky is that you need a mix of lengths to go with skirts vs jeans. I think tops are one area where you could have a lot.
1 dressier blouse
1 white collared blouse (assuming you like this look)
1 vest
3 camis
2 pairs knee high boots - one with heels and one without
1 pair ankle boots
2 ballet flats
1 converses
1 sandal
2 pairs of dressy heels
4 bags (one cream, one black, one in a cheery color, and one clutch)
3 bras
7 pairs undies
2 bathing suits (you need more than 1 if you are in the water with the kids every day)
This is an accurate picture of the items I wear the most. Jeans - I have only 1 bootcut and I have two trouser cuts and two skinnies instead of one. I have a LOT of tops, about half are dressier fabrics and half are knits, but I have more dressy occasions and my kids are older and not so messy! I wear most of my tops too - those that I don't wear often enough, get culled out. If I could only live with 6 cardigans, I could probably do that. I do have more blazers than this, but again, I also have more occasions to wear them.
You'll see I don't list dress slacks at all. I do have these, but I find I don't wear them very often anymore, so I scratched them off the list completely.
As a SAHM of young kids, I suspect the bulk of your wardrobe is going to be in jeans and machine-washable tops, and flat comfortable shoes. If you wanted to pare down the number of jeans, then just choose one style of jeans and stick to that. You don't really need straight, skinny, AND bootcut. Although I guess you need skinnies if you like wearing them tucked into boots in the winter.
Bare minimum? I would say you could probably get by with only 3 jeans, but it sounds like that's what you have and it's not working out. I would take whatever pair you wear the most often, and duplicate them. I duplicated by COH huttons, so what I do is when I get around to wearing the second pair because all the rest of my jeans are dirty, that's when I know to do a load of jeans.