Don't be sad about "not being an SAHM." As others note, you ARE still an SAHM but now the really good stuff begins!
Volunteer! Get into your kids' schools. You have an older child, I take it, but maybe having the younger one at home has prevented you from doing much at school--?? Now you can really help out. Kindergarten teachers usually need a lot of parental help -- cutting out a lot of cutely shaped covers for little books, or assembling those books, or helping the kids make Pilgrim hats at Thanksgiving, or shepherding a field trip. In the early school years, about grades K-2, the teachers will be craving parent volunteers. And look beyond your own child's classroom to volunteering elsewhere in the school: The school office may have a system where parents can come in to do photocopying and collating for many teachers. Or the art teacher may need help with organizing supplies, especially early in the year. Or the cafeteria may need volunteer parents to help out at lunchtimes (our old school had a roster where certain parents helped just one or two days a week, not serving food but in the cafeteria itself, helping kids open packages, handing out spoons, etc.). Join the PTA and get involved in the bigger issues of budget and programs if that's your thing -- you may be great at it. In other words, school is now a huge part of your "SAHM" life.
And here's the best part: If you volunteer at school and become known to teachers and office staff there, it is good for you and for your child. Your child knows that school is a safe place because mom is there; your child learns that it's important for adults to participate at school, not just drop kids there and walk away; and you will be plugged in to what's really going on at school. You'll learn whether the budget really is enough or where there are holes; you'll learn sooner than other parents which programs are under threat in the next budget year and can write letters or mobilize others to save art or music or whatever may be under threat; you can see teachers at least a bit in action, and get a feel for whether Mrs. X or Mr. Y really would be the better fit for your child year after next. Best of all you can get to know their classmates and classmates' parents.
And don't forget, as your kids get older, "SAHM" will include chauffeuring them to their activities -- art class, dance class, sports, whatever. And you can get involved with those too. I volunteer for things at my daughter's dance school, where parents are needed to help with lots of things in order for shows to happen.
You're feeling those lovely but sad feelings of the kids going off to school. But you are moving on now, too. Don't miss the terrific opportunity to use your new free time to get involved in school and activities. You will be glad you did.