My 2 cents only - YMMV and this advice is worth what you paid for it ...
Of course you can go and fly somewhere else, and it should be good for you; handling a different aircraft and different airspace etc. should give you a different perspective and broaden your skills - even if you are pre-solo. I went for 3 sightseeing flights whilst on holiday when I was pre-solo - there happened to be a flying club in the vicinity and one of their instructors was happy to take me (and my partner) up for some sightseeing trips. He duly never touched the controls - and it was great
HOWEVER (1) - it may not be good for everyone. Some people get upset if their routines change and depending on you and your personality/skill set, the temporary setback with a new aeroplane and airfield, instructor etc. may do more harm than good. Your instructor will have an opinion on this and you should talk to him/her.
HOWEVER (2) - what you seem to really be asking is whether you can do it as part of your training and count it towards your 45 hours, and that is a different question. Even if you go somewhere within EASA land and get an EASA approved instructor to sign off your hours AND you get to learn some meaningful new skills after getting used to the new instructor/aeroplane/airfield, it is ultimately your existing school which needs to approve these and which, after they believe you have achieved the right level, will put you forward for a skills test, irrespective of the number of hours in your logbook and the number of exercises which have been signed off by someone else... The amount of business they will lose by you going elsewhere for a couple of weeks is likely to be minimal. But you still really do need to talk to them - they may be able to talk to your interim instructor and make it more likely that the extra flying will be useful to your development.
Going back to my 3 hours sightseeing, these hours were 'wasted' as they did not count towards my 45 hours and, since I was neither PUT nor P1, I was really just supernumerary, so they still don't count for anything. But I flew them 'in my heart' and they gave me some excellent experience in a completely different environment. And they were fun
In fact, so much fun was it that, by the time I passed my skills test, I had about 8 hours of 'wasted' time in my logbook (duly marked as such) in 4 different aircraft from 4 different airfields in 3 countries on 2 different hemispheres
- in addition to my normal flying lessons.
Personally, I think you are barking up the wrong tree for 3 reasons:
1. Flying elsewhere is good practice (with the caveat mentioned above) but you should not see those hours as part of your training, but part of your general flying experience, whether or not they count towards your 45 hours. What they will do, though, is keep you more current, so that the hours you do fly at your normal place should be more effective.
2. You seem to have no faith/confidence in your instructor/school to be able to do what is best for you, thinking only of their own short term. If are right, you should change schools regardless of any other factors. However, I think you are probably doing them a disservice and it sounds like you need to work on your relationship with them. You should show some faith and discuss this with them. And even if they say that they would not recommend it, there may be a reason for that as well.
3. Fly whatever you can, wherever you can, for the fun of it - not because it makes sense or it is cheaper - but just because it is fun and it is flying !
B.