I think the reason they don't talk a lot about Tim's mother on the show is essentially practical. Since this is an ensemble show and not focusing solely (or even primarily) on the Turners, it has to concentrate on the elements of their story that are most relevant to the show. Mrs. Turner #1 exists primarily as exposition, and since Mrs. Turner #2 (Shelagh) is a major character on the show, it's her relationship with Patrick and Timothy (and theirs with her) that is focused on when there is time for a family scene. Dwelling too much on the first wife/mom, or any exposition character would detract too much from the story of the show, which is primarily a medical show and not a family drama, and that story also has to move forward.
Still, in terms of what we have been shown (supplemented by other official sources I'll mention), I don't think there's been an indication that they aren't allowed to talk about Tim's mother. They do talk about her at least once--in series 2 when then-Sister Bernadette is in the sanatorium and Patrick is shown sitting in the car looking sad. Tim, who is in the back seat, asks his dad if he's sad, mentioning his maternal grandmother's ("Granny Parker") saying that Patrick had acted something like that after the first Mrs. Turner died. Also, in the first Christmas special, Patrick did mention the time frame to Sister B. He said "it's been almost a year" and "it will be the first Christmas since his mother died", putting the first wife's death somewhere around January 1957 (before the start of season 1).
The show also gave Tim and Shelagh a common bond even before her romantic relationship with Patrick began (they both lost their mothers when they were young children---Sister B mentions this in the same scene in the first Christmas special after Patrick talks about how long it's been since his wife died). I think that connection somewhat informed the relationship that grew between Timothy and Shelagh even before she officially became his stepmother. She was also shown to have a good rapport with children and it seemed that Tim was completely on board with her marrying his dad (he even wrote the proposal note). There were indications that she was having difficulties learning how to be a parental figure to him after the marriage, though especially in the first half of the episode where Tim gets his leg braces taken off, although they made great progress in that episode, and by the end of series 3 Tim was calling her "Mum". I'm fairly sure the first time he does that is in the last episode of series 3, and it does seem to be 100% voluntary.
The show, and especially with the Turner family, seems to have been emphasizing the idea that family is about more than just biology. I think Tim sees Shelagh as his second mother--not diminishing the first (who he will always remember), but still Shelagh is his primary maternal figure now, and he loves her as such. She's the one who will be there as he grows up, and if and when he eventually has children of his own, the only grandmother they will know on his side will be Shelagh. I think step-families are different depending on the people involved and the circumstances. In the case of a widower with a young child marrying a woman with no children of her own, I think the relationship is inclined to be more traditionally parental than in the case where there was a divorce and the biological mother is still around and involved in the child's life, especially if the stepmother is inclined to love the child as her own, as Shelagh clearly is (and stated this in episode 7 of season 4) and the child fully accepts the step-parent (which has also been indicated on the show). The Turners also have Angela, who is adopted and not biologically related to either parent or Timothy, but they are her family. Patrick and Shelagh are the only parents she knows and Tim is her brother just as much as he would be if they were biologically related. I think the fact that this family is shown to be so happy and well-functioning and clearly loving even though they are not strictly speaking a "traditional" family is a major theme of their story on this show. They demonstrate that families are about love and choice as much as (or maybe even more than) about biological ties. It's not saying biology isn't important, but that it's not the only important thing.
In terms of what was the accepted practice at the time for how children addressed step-parents, I'm not sure because I wasn't around, but looking at pop culture references (like the The Brady Bunch from the late 60s/early 70s, and The Sound of Music film from 1965) it did seem that children calling a loved step-parent "mom" or "dad" was not unusual, even when the child is a teenager when the parent remarries (Liesl in The Sound of Music calls Maria "Mother" after the marriage--editing to add I know this film is set in the 1930s even though it was made in the 60s). I personally have known people who called step-parents by their names and those who have called them "Mom" or "Dad". I think it varies depending on the dynamics of the relationship and what the child wants.
As for Mrs. Turner #1 there is some backstory about her in the latest Call the Midwife companion book, Doctor Turner's Casebook, which was written by Stephen McGann (who plays Dr. Turner) and with a foreword by show creator (and McGann's real-life wife) Heidi Thomas. It's not a lot, and there's a lot more information about Shelagh (because she's much more relevant to the actual show), but it does say her name, how she died, and does indicate that Patrick and Tim did talk about her after she died. I don't think they talk about her on the show much because there isn't time (and also because like in real life, a family has to move forward. It's important to remember the past, but you can't live in it). She has been mentioned a few times, but only when it's been relevant to the current story--like when Tim found the picture of his mother. While that story wasn't given a lot of time, what I took from it was that Tim was conflicted about showing the picture to his parents because he didn't want to make it look like he didn't appreciate Shelagh, but by the end of the episode he'd been reminded even more that he has a loving second mother in Shelagh (that's the episode where he overheard her saying she loved him as much as she would if she'd given birth to him, which made him smile). He clearly wants to remember his first mother, though, so he gets to keep and cherish his memories of her, but he's also got a life in the present and the future with a family who loves him.