Has it been confirmed that this is what it is?
Assuming that it has been, genital hsv1 doesn't shed nearly as often as genital hsv2, and doesn't recur nearly as often. Many people only get the initial outbreak, and then never get another.
Shedding rates: (and you can find all this in the herpes handbook - https://westoverheights.com/herpes/the-updated-herpes-handbook/)
HSV 2 genital 15-30% of days evaluated
HSV 1 genital 3-5% of days evaluated
HSV 1 oral 25% of days evaluated
HSV 2 oral 1% of days evaluated
Did you also kiss the person you got hsv1 from? If you did, it's possible you got oral hsv1, too.
So for transmission rates. We don't know the exact transmission rates for ghsv1 - it hasn't been studied, but here are the rates for ghsv2, and if your math is better than mine, maybe you can extrapolate some figures.
The transmission rates for hsv2, male to female, over the course of a year, assuming sex 2-3 times a week:
Only avoiding sex during an outbreak - 8-10%
Adding condoms OR daily suppression - 4-5%
Adding condoms AND daily suppression - 2-3%
Chances are excellent that you won't transmit it.
As far as oral sex goes, herpes of either type doesn't seem to go from the genitals to the mouth like it goes from the mouth to the genitals. It's possible, but not at all likely. I'd avoid oral sex - or any sex - if you have an outbreak, though.
As far as your kids - are these children already born? If they are, unless either of you are having sexual contact with them, there's no concern.
If you are concerned about pregnancy, then the only risks are her being infected during her 3rd trimester or if they are delivered while she has an outbreak.
Are you considering not telling her? I think that's a really bad idea. Ordinarily, I lean towards not confessing cheating to unload your guilt because I find that self-serving, but now we have an STD in the picture, especially if you are planning on having (more) children.
However, she could have hsv1, and been the one to give this to you if she performs oral sex on you. You could have had it before you entered the relationship and just now gotten an outbreak. While I am not an advocate of lying, there are ways around telling her you cheated and still telling her you have this, which is more important to me. You could have had suspicious symptoms in the past that a doctor said were fungal, like jock itch, but may have been herpes, and never knew. (That legitimately happens all the time.) That would be preferable that letting her think she gave it to you.
She can test with a type specific IgG herpes blood test to find out if she has type 1. About half the adult population has it, and 90% will never get a cold sore. If she has it already, she can't get it again.
Does that make sense?