I'm reading this thread with interest as I'm a solicitor and had my first child early in my career (admittedly at 1 year PQE rather than before TC).
I've had a look at BPP's site and it seems there is an option to do the PGDL with a top up module which escalates it to an LLM. I'm guessing that is what you did hence your remarks about not needing a GDL.
If you do a TC you will need to fit in the LPC before you start (funding it yourself if necessary). Bigger firms in particular often recruit two years in advance but traditionally this is in year 2 of a degree so the two year "break" is for the final year of uni and then one year FT LPC; it's not really a "break" at all. At my firm candidates who can start sooner are often not given the full two years. Even if you secure a TC with full two year wait, it's still not a spare 2 years to fill (with a pregnancy and baby for example!) as you need to spend either a year FT LPC or two years PT LPC.
If you do the SQE or CILEX route you don't need the LPC, but if you start one of those routes now, there won't be a starting "break" at all either.
My recommendation would be to start paralegalling now + looking for a SQE or CILEX placement. Paralegal work will bring you (a) income, albeit modest (b) experience in the legal industry and (c) useful stuff for your applications which may possibly be at the same firm you are paralegalling for. Once you are formally employed and are building up maternity leave rights you can consider how/ when a second child might fit in with your qualification path. Otherwise you'll just keep drifting.
I'm advising, I think, steering away from the TC path for various reasons . As PPs have said TCs are now SO hard to get, even harder if you want/ need a firm who funds your LPC. I'm on the recruitment panel for my firm and honestly the calibre of candidates is so high, we turn away so many people who are eminently capable because there is one place for every 20+ applicants. When I applied (1999) it was more like twice as many applicants as TCs!
Some people keep applying for years to get a TC (and some never succeed). That's a long time to be in limbo while you wonder when it's "safe" to have another baby without scuppering your chances career wise.
I will also add that your chances of getting a TC (or indeed SQE or CILEX placement) will be vastly improved by work experience, hence my advice to get paralegal work ASAP. It will help your CV stand out among other identikit ones with a 2.1 and LLM.
Practically speaking it is HARD to work in law (particularly litigation) with small children. It's possible but it's tough especially as a junior as you have to work to the timescales, appointments and tasks set by the senior lawyers. When I had my first child I went back FT after 4 months. I felt I was likely to get quietly managed out otherwise as I didn't yet have the experience or client following to give me any unique "value" to my employer and there was a very keen (male) NQ who'd taken over my cases during my ML and was clearly pissed off when I returned so quickly. I spent little time with my son during the week. I had to "make it count" during weekends and annual leave. I don't think it harmed him though as he's now nearly 17 and planning a law degree/ career in law himself!
Then there was a lovely interim period where I was more senior but had control over my own diary etc. During these years I had a second child. I was still FT but the work/ life balance was much more manageable.
Then I became a partner and the extra responsibility has piled on the hours and pressure again, not least because I'm directly answerable to clients (as well as line managing two teams, business development etc. ) Thanks to covid though I'm now WFH 50% of the time so at least I see more of my kids even though I'm often in front of a laptop! This is a city firm but not top commercial one, mainly insurance clients and supposedly with a good work/life balance. To be fair if I hadn't gone for partnership it probably would be.
One last thing. You seem reliant on your partner financially. You should really protect yourself with marriage especially if you bear the burden of primary parenting and household stuff.