As someone who was 'brought up Brethren', echoing what others have said - that if they were Open Brethren, it wouldn't be a big deal. They might well have 'shopped around' for churches that suited them.
My great-grandfather was the one who started us off in the denomination, around the time your family were growing up, and he attended both the Baptist Chapel and the Brethren Gospel Hall for many years.
If your family were brought up in the Brethren church, there probably wouldn't be much to tell you - Brethren don't practice infant baptism/christening, they have adult baptism (and even if someone attended for many years they might not ever get baptised). I'm not sure what records the Brethren kept then, generally or locally, and they may well still retain them today (where they're still going).
Meeting places are officially 'Gospel Halls' although in practice we often just called ours a chapel anyway. They don't have ministers - ours had a group of members (all the adult, baptised males) who formed an 'overseeing' committe (known as "the Oversight.") We had a communion service in the mornings and a gospel service in the evening, which is pretty usual, but there is always a communion service weekly (wiki says 'remembrance services' although we called ours 'the Breaking of Bread'.*) The communion service is not led by any speaker - in theory like the Quakers where you wait for inspiration, but in practice (when I was a child) it was pretty formulaic (and had music). People who moved from one branch to the other would take a letter of introduction (which said whether or not they'd been baptised and could take the communion).
We had a Sunday School & Bible Class and also a Youth Group, so your family could easily have just attended something like that for a while.
Re. marriages - they were held in the Hall, but attended by the registrar and only recorded in the Register Office; so they have no registers (unless someone gets licensed, but generally, given the minister-less situation, that's less likely with Brethren than other non-c denoms). My parents were married in the Brethren Gospel Hall by one of the members, legalised by the registrar present, as did my aunt and uncle.
Wiki's Open Brethren page has some links to Brethren organisations at the bottom, which might possibly help in trying to find if there was a local Brethren hall to your family at the time, or maybe would know about records, if any:
http://www.gospelhall.org.uk/ -> for finding a current Brethren place where your family were. if they still exist, you can contact them about if they have any archive of newsletters or other records that someone might be able to check for you.
https://www.brethrenarchive.org/http://www.brethrenhistory.org/(I attended in the 1980s, but ours really hadn't changed much since the 60s when my parents went there - except maybe to grow more conservative rather than less, so some of the things would definitely have still be very similar in outline.)
* My Dad one time abbreviated this as "B&B" when doing the announcements and ended up with: "On Sunday we meet for Bread and Breakfast as usual." (HIghlight of the year for everyone but poor Dad, of course.)