OP, I think there's a gap in the market there, tbh.
I work full time but am self employed, and work from home, so I see a lot of other mums at mum and baby groups/soft play/in the park etc during the day when I go with DS. I'd say they are 'mum friends' in that I only know them because I see them at these places, and we've met because we have kids.
I've met some lovely people and other mums are a very good source of info about activities/schools etc. The other mums are all either working part time or SAHMs, for the time being.
For friends who work full time with small children, they only seem to have the chance to meet other mums at pick up and drop off at nursery, and then everyone's on a tight schedule, and it's not like chatting in the park. Really, their only chance to do a mums outing, with other kids, is going to be the weekend... but I think you are right, weekends for most families do seem to be nuclear or extended family time.
I guess Saturday morning activities might be a way to meet other mums with a similar schedule and see if they are more flexible about weekends... I know what you mean, though, it is hard. I'd meet up! my weekends aren't any different to my week days tbh - I have to work part of every day to manage the work/parent thing but in practice that means we don't have 'nuclear family' weekends.