Adding up Transformer Output
I have some observations and a question.

1) input power is 25 Vac, 5A.  That works out to 125 VA.

2) Transformer #1 is 220 Vac, 0.5A.  That works out to 110 VA.

3) Transformer #2 is 6 Vac, 20A.  That works out to 120 VA.

4) Your desired output is 250V 20A.  That works out to 5000 VA or 5 kVA.

As you can see, the numbers between input and desired output don't match up.  What you are asking for is not possible.

Now for my question: 

1) Exactly HOW are you arranging things so that only one transformer gets input current alternatively?