Can only answer what I think I'd most likely do as I've not actually ever done it.

I would likely write a letter but tell them in person. The purpose of the letter would be to detail the pertinent information, when, why, how, etc. I think I'd feel I owe it to my clients to tell them in person, and I'd imagine their heads would start spinning about their future child care. Although they might ask questions, I'm not sure how much information they would hear as their minds would be filled with so much. The letter would clarify details once the initial shock had worn off.

I would avoid stating it in front of the children - so it might be a phone call in the evenings if that's not possible at pick up/collection. Children don't belong in adult conversations anyway but I would allow their parents to find some solutions and choose when to share the information with their child. If you tell the parents in front of the children, it removes their ability to reassure the child with facts and all they can offer is supposition.

How much notice - As much as possible. I would think it's far to double your notice period as a minimum. I would also be tempted to have reached out to local providers I respect and if they have vacancies, I would pass their contact information to the parents as someone I'd recommend.

Check how your contracts are worded. Mine say "either party may terminate for any reason with one month's written notice. Fees are due regardless of attendance during the notice period". So I'd give mine two months if closing, I'd be willing to work an extra weeks or so (depending on reasons for closing) if someone has yet to find alternative care but I wouldn't necessarily announce that from the beginning. I'm lucky in the sense I've always managed open communication so I think in this situation, someone who is struggling to find care, would likely have told me and I'd know if their reasons were valid or resistance. I could then decide if I would extend the closure for a couple of weeks for their child.

In terms of reason - it depends how personal it was. If the reasons are personal and you aren't ready to share, a general statement that your personal situation has changed and you are needed elsewhere, is sufficient. Don't feel obligated to share more detail that you wish to. You don't have to answer every question people ask.