I'm not in the estriol/Copaxone trial but I've been on estriol/progesterone +Copaxone for about 3-4 years. Before that I was on Avonex with estriol/progestrone (diagnosed 7 years ago). So far so good, I also "do" exercise, diet and supplements.
The only side effects IMO have been from the DMDs--in retrospect Avonex made me worse (I wanted off it after 6 months but persisted for a couple of years) and Copaxone side effects are primarily injection site related.
Here's a link to the estriol
thread which has info mostly about other hormones.
Please let us know if you decide to enter the trial and how it goes. It's been a long, long time and lots of effort trying to complete the trial since there's no pharmaceutical company issuing press releases every other day.
Here's a link to an article that describes some of the struggle. Quest for an effective MS treatment stymied
finding a way to underwrite costly research that won’t necessarily have a big payoff is about as easy as finding a miracle cure
All the best to you.