I have done this in the past -this is the second time i have been a widow - we both had a daughter each who were at school together and were drawn together as friends because of their losses - and Keith and i were also drawn together through the same thing, supporting them, taking them for days out, and supporting each other with the general issues teenage daughters can wreak - so we were also friends and nothing more than that for a long time. My other daughter was living close by so she was aware of the friendship too - he had two older grown up children and a step son as well. Being friends first and being known to each others children well in advance of it becoming anything else helped as did making it clear that i was not a threat to the memory of their mum nor him to Mark.Thats not quite the same as having a "date" i know but if you know who this person is perhaps you are already friends and perhaps the transition will be the same. It wasnt straightforward we knew there would be issues particularly with the step son who was already suffering from all the changes he had been through in his life - but it didnt create a massive rift in his relationships with them because they were all told we were not trying to replace them, and we each understood that the other would always cherish and love the ones we had lost, but this was a differnt relationship and it is possible to love two people.
as you say you havnt asked yet and she may say no, and she may say no because she feels three years is not long enough for you to be thinking straight, and that this is a rebound thing, - that perhaps depends on her own life experieces, and how well you know each other now - If she does that then dont feel that is a rejection of you as a person, it perhaps is a sign of her regard for you, not wanting to wreck your friendship with a relationship that went wrong because the timing was wrong, so again think of it as something two friends can share, keep her in your life you can always ask again later.
If she says yes, then a "first date" will perhaps tell you whether you want more than that, so maybe if you make it something that you can play by ear at the time - maybe tickets for a concert or something she enjoys doing, rather than an intimate candle lit dinner might be the way to play it.
You may find the children, even the one at home,are pleased for you,because they are concerned you will end up lonely, but if you are up front and say - the first time you are doing - whatever you decide to do - with the persons name - and it turns out not to be right for you, then they have nothing to be concerned about - if it is a date which becomes something more, then explain too them that it doesnt take away anything from theirs or your memorys of their mum, she isnt trying to replace her, doesnt expect to be called mum etc etc then they may well be fine about it, you cant really know until you ask.