Morning,
Hope you are feeling better. It's so grim having anything extra at this surreal time and place in this. I wrote the longest post on Saturday night vi iphone but it hasn't appeared and I had to calm down for a day else it would have looked like I was cross and abrupt for all the wrong reasons...You are getting v good advice - props to Laurierf and BalloonSlayer especially.
I also suggest a quick call to the lawyer you like regarding any experience of overnight access and young ages. More in a sec on that.
Mediation is your friend OP - that's not to say that it "goes your way" but it puts your DTs back in pole position - in fact I recommend that you bring a photo of them to mediation. Make real the two little souls also affected by daddy and the cock chobbler's selfish acts and that - through you and the mediator - their best interests can be worked out in this new raw change.
Mediators will have heard every star struck-lovers-held-back-yet-more-by-the-jealous-ex story. It holds no sway (neither do spurious reasons of a hurt ex either to be fair) and they are good at their job and focused. That said - anything unpalatable that gets said - don't feel railroaded (or expect him to think nicely of you if you agree!) have a mantra along the lines of "I will take that notion away and think on it for a few days."
You have a reasonable right to satisfy yourself that this relationship of theirs has legs post exposure (it is, imo, important that you discovered the relationship and all this is a consequence of that - you have no knowing what/if it might have been revealed and, as a consequence an end to your marriage or not.) Without the oxygen of the thrill of secrecy there have been well documented high percentages of this fizzling out.
KEY - and mediation should stress it - is that DCs shouldn't be used as messengers. The day if/when they are to meet OW you should be made aware prior to it so you can compose yourself - and make their little world ok (even if yours isn't - wine/friends/counselling/sleep aid for that). Ie they come back and say we met OW and you can say - yes daddy said you were going to the park, how was it? Instead of trying to reign in shock/anger/nausea which will make them think they have done something to you.
It is hard. And please be brave - try to be rational and listen, make notes (although a summary will be sent) and not make snide or teary remarks etc. Try to hold together and not be emotional (it's not pleasant sitting opposite an unrecognisable rancid stranger who once was your lovely husband).
star tip Go in solutions based ie You understand and will help to ensure your DTs have a healthy stable relationship with their father as this is best for them and he and they love each other. You see this, at their age, and on sound research and legal advice, as little but often at this stage and so you propose 2 afternoons + tea with a return to you at bedtime (perhaps - I did - you can go for a small walk whilst he puts them to bed but you may not be able to suffer him anywhere in your space or he might riffle through stuff). And you will review this in 6 months in this forum to ensure both he and YOU keep DTs needs uppermost. You know that he loves the children and will want their the best for them and YOU have had time to research what that best-for-them is, and with help of you - lovely mediator (ie he has been too busy having penis attended to to think of anything else.) You will not, however, be green lighting a holiday with OW at this stage so October is off permanently and, for future ref, you will need to be consulted on times and not have hand forced by a booking being made and then you told - this is not to put a spanner in the works but to ascertain that they are well/nothing going on re nursery that needs dealing with etc/you yourself have not made plans
What are the Dts personalities Ophelia? That too - has a bearing on when is right - a shy DC will adjust less well allegedly than an outgoing one.
Also - more key now before he jumps the gun with week long holidays - is what they know re their home life and how it should be told with respect to their age. That is first and should be the bulk of the meeting!!
My Dcs seemed to be offered as yet more gifts to the fabulous OW. The final gift if you like. Not to say he doesn't love them but the cock waving that happened re access was male swagger and based on this to begin with.
Three last things:
I would say you wish to have documented that, whilst he may well admire (although has he even seen it!!) OW parenting, it is you and he only involved in DT parenting.
Do consider docs for sleep aid/anxiety. I took citalopram and it helped enormously (not for depression but anxiety - took a while to learn to switch off as wasn't used to being sole adult sleeper in house so twittery.) Also it helped calm down the pecking night-birds of what-now?, money, job, house, work that get to your head in the 4ams.
Finance and access are separated into different sessions ime. Prevents any trading which is held in v dim view. I am sure your lawyer will have mentioned but a court can order a sale not to take place until the youngest is 18 or left full-time education whichever is the latter. I would suggest he gifts his half to the DTs to show a long term financial commitment!
Hope it goes well and there is some comfort at the end from having some ground rules in place that you were involved in.
When is it?