If this is the C of E, then unless you have a really busy and well-supported church on your doorstep, then yes, most of it happens on a Sunday. But some churches have parent and child services on a weekday morning (generally those attached to a church school) or they have parent and toddler groups in the hall etc
At our church, what happens if a new person comes is this:
they are welcomed and given the information they need to attend the service
during the service they will be left quietly to their own devices to take it all in, except during the Peace when various people will shake their hands
if they are not sure about going up to have a blessing or take communion someone will be sure to see that they get guidance
After church someone will be bound to tell them about coffee in the church hall, whereupon other parishioners will introduce themselves and chat to them
Our church is nothing special - not smart or well-attended (= generating £££ for Southwark Diocese ), but its welcome is incredibly friendly. Dh was ill at the time and I went for the first few weeks on my own with two young dcs. Everyone was so kind to us. : dh is now Churchwarden and I sing in the Choir and help with Sunday School . More importantly we feel connected with the community in which we live and have made some really interesting friends of all ages.
If you are at a low ebb because of a bereavement, the right church will give you comfort and fellowship without making demands you don't feel you can deal with at the moment.
Good luck - I think you need to pluck up courage and walk through a door one Sunday. Check out noticeboards and be alert for signs of especially family-friendly services and activities. Ring the Vicarage if you can.