bubbling toilet / vent stack issue?

Hi all.
I know I've posted on this before, but a lot has changed. I need to hear best guesses on solving this problem.

The drain pipe in my house is a Y configuration. On one side is just the kitchen and on the other side is the master bath. Washing machine drains outdoors. The second bath is on the stem where the Y comes together, and it is another 50 feet or so from there to the septic tank.

I posted earlier this year about problems with air bubbling up and sucking down in the toilet bowl in the master bath. Since this was after I replaced a lot of pipe, I figured it was something I did wrong. I then installed two vents in the second bath, one on the 3" pipe that catches the toilet and bath water and 1 on the sink. These join and go up and out the roof. Thought the problem was solved, but when my Culligan machines cycle at 3 in the morning, I occasionally hear glugging in the master toilet. The 2nd bath currently has no sink or toilet as I'm still remodeling, but there is a bathtub that I do use.

I figured there was more to the problem but decided to live with it for now. Then family came to stay and now when they use the bathtub in the master bath, the toilet just downstream of the tub bubbles hard, alternatively pulling all the water out of the bowl or sending it to the top of the bowl. I think the issue is that more people using the bathroom is exacerbating the problem.

Lastly, I'm pretty sure that there is no vent pipe in the master bath. As it happens, though, I'm remodeling next to the master bath as well, and it is a perfect time to put one in. I'm trying to figure out the physics of the problem and 1) is this a vent problem (can my vents on the other side of the house and the one in the kitchen suffice for the house) and if so, where should the vent be positioned to solve this problem and 2) could this be a clog caused by something like a sagging pipe? The reason I ask this is that before my company showed up, the problem was happening only in the night and resolving itself within hours. Again, I don't quite get the physics of the problem.

Open to best guesses. I intend to add vent(s) this weekend.

Thanks.