Can I exit and reenter a UK station while waiting for a connecting train?

The actual barriers might not open for you, (those in Bham New St never open when I change there, even when you have to go through them to go to your next platform, but Liverpool ones do), but if you show your ticket to an attendant they will open it for you to let you in/out, I've been doing it for years using TrainLine and never had an issue with it! If there are no attendants around to open it, I've asked security or people on the ticket desks who have either opened it or got someone to do so.

If it is a small station, there is also a chance it doesn't actually have any barriers, my home town and the ones around don't have any, and some of the larger ones like Preston don't either.

You can as confirmed by an email from Trainline:

I would like to inform you that whether you can break or not break the journey depends on the type of ticket you've booked. Anytime, Off-Peak and Super Off-Peak tickets are more flexible options, so breaking your journey is allowed, as long as you don’t start your journey before, or end it after, the two destinations that are written on your ticket.

Checking the terms and conditions of the ticket you bought will provide more information. If you have an Advance ticket, breaking your journey’s not allowed, unless it’s to change to/from a connecting train, which will be written on your ticket.

All tickets allow break of journey for connectional purposes i.e. changing trains where necessary. If you have a waiting period in a station for your connecting train, you can pass through the barriers or leave the station during that time.

In my experience that's always been allowed for trains I've taken, I don't use trainline, but assuming you get the same orange and cream credit card sized ticket as every other train ticket this should apply. I often change trains, wait at stations and even get on or off at stations between my specified start / end station and have never had a barrier not open for me. In some stations you have to go through ticket barriers to change train / platform or get to a waiting room. And even if your ticket didn't let you through barriers (which may not be present or operational if it is a small, explaining your situation politely to an attendant would almost certainly result in you being allowed to leave the station and return.

Note: my experience is limited to South Western Railway, TFL and Great Western Railway, YMMV on other carriers

I would consider buying two return tickets - for the two parts of your journey: one from your origin to your connecting station and another from your connecting station to your destination. That way you'll have the right tickets to get in and out of your connecting station regardless of it being manned or having barriers.

There's a chance it won't cost you anything extra. (Bizarrely, splitting some rail journey can even make them cheaper.)

Probably. If you show your ticket to the staff at the barrier and explain, I can't imagine you will have a problem - I've done this dozens of times. Make a point of re-entering the station at the same barrier, you'll be recognized and waved through.

Technically some tickets don't allow it (most do), but even then a polite ask will almost always get you through.

Obviously if it's a station without barriers, no problem at all.

Find a station very close to the one you will be waiting at, buy a return ticket from and back to the nearby station for roughly corresponding times, will cost about £2-£3. Use those tickets to exit and re enter the station and then bin them and continue your journey. Sorted