I have a strange plumbing problem. Often, but not always we will notice that when it rains the main bathroom toilet will not flush well.(It seems like a lack of pressure) We could live with that. Second, occasionally the washer can't handle the drain cycle and will back up and spill. We can live with that. Now in Houston we haven't seen rain in months. Just last week we had two days of rain. Since then the washer won't drain. And both the main and master bedroom toilets are gurgling, filling up/sometimes over flowing when the washer is running. The tub in the main bathroom is also back filling with dirty water, when the washer is draining. How are these related and what can I do?

City sewer or septic? Gurgling most often means a ventstack is clogged. That will cause drainage problems and the sound.

City sewer

Is the rainwater runoff connected to your sewer main? Do you get a back up out of the floor drain? Back to you, Tom

I don't know but I am beginning to suspect that the rain drain is connected, although I am pretty sure that would be against code. And yes I get back up in the floor drain in the master shower and the main tub. (the only two floor drains)
Thanks

The first thing I would have done is to check where the rain water runoff goes to and disconnect and reroute the rain water outlet. Failing that I would install a check valve,(see image) just downstream of the house cleanout to prevent backups coming in from the city maiun.
Let me know what you think, Tom