Hellooo. Can totally sympathise as ive been in this situation, Me and my DP went 1 year with just seeing each other properly for 1 night a week and then I felt like I was a mistress or something when he would leave me early in mornings for work, what with both or parental duties, both our work it was so bloody hard. We are now living together but I wouldnt advise it just for the sake of seeing him, it felt like it was the next step for us after I found out I was pregnant.
I cant really suggest anything to help you as its your personal situation what works for one doesnt another, but can list a few things we used to do to try and spend time with each other.
He drives past my house on way home from work so would nip in for a coffee 2/3 times per week, was awkward at first as the kids only knew him has my friend
We would meet up for a date in a pub with a play area, the kids just thought I was meeting up with my friend. Also met up a few times with his son and my kids at soft plays on a Saturday if he wasnt working.
My kids are usually with there dad on a weekend and thats when he has his son not always a full weekend but at some point he would be with him, he lived with his parents so luckilly they would help him out quite a bit while he was working and occasionally his mum would look after his son so we could go for a meal or something.
On a sunday afternoon we would try catch a couple hours too if we were child free or not working we would just go for walks in the country with the dogs or out for Sunday dinner or something. Sometimes just watch a dvd snuggled up :)
I realise my situation is different and the kids knew him before via our next door neighbours so he wasnt a total stranger they just thought we were friends. I know its good to keep kids and partners seperate but I imagine once you have all met each other it might take a bit of pressure away? I appreciate too that the distance is a problem, could you ever meet half way just for a couple of hours or something?