I don't think £350 a month is much, tbh. Because you have to fund all of your "one offs" from that.
Like:
Birthdays
Christmas
Car repairs
Anniversaries
Valentines
Easter
Play dates
School trips
School books/materials
Kitchen white goods break downs
Boiler servicing/repairs
Home repairs (leaks etc)
Hobbies
Extra curricular activities for kids, like swimming
Dentist
Hair cuts
Shoes
Clothes
And so much more besides.
However....being stretched is just a reality when you have 2 kids needing childcare. Almost everyone has that 5 year stint where things are tight. When I went back to work, after I deducted child care, I was working for only £140 per month.Which is sickening, however, it meant that my job was kept open.
Long term, you'll have no child care at all, and you will have £1935 left per month for treats and "one offs", which is exceptionally good. This is what you need to focus on....the end game, as it were.
Fwiw, I find that "one offs" add up to a lot! In the last 7 years or so, I've had to find money for god children's 18th's, godchildren's 21st's, my own children's 18th's and one of their 21st's (the other will be 21 soon), parents 60th's, parents 70th's, siblings 40th's, In-laws 40th's, Partners and my 40'ths, births of neices and nephews, Christenings, a few weddings, lots of car repairs, massive (almost £3k) vets bill for an uninsured pet....the list goes on and on.
I guess you could just not buy a sibling/child/neice/nephew anything for their "big" birthdays, but how shit would that be, when everyone pooled together when it was one of your big birthdays?
On paper me and DH should have a good sum of money left over after all bills are paid, but there is always something needing paid, and we never save what we should be saving on paper!!