1. Ty1 and Ty3 are allelic and you want to backcross BOTH into an elite cultivar:
(1) You can first make a cross between a resistant line (Ty1/Ty3) and an elite line (-/-)
(2) Ty1/Ty3 x -/- : your progeny will have either Ty1/- or Ty3/- genotype
(3) Backcross Ty1/- several runs with the elite line (-/-) to regain elite line genetic background (select the exist of Ty1 allele after each backcross). Let's say the find product is Elite line Ty1.
(4) At the same time, backcross Ty3/- several runs with the same elite line (-/-) to regain elite line genetic background (select the exist of Ty3 allele after each backcross). Let's say the find product is Elite line Ty3.
(5) Make a cross between (Elite line Ty1) and (Elite line Ty3); select progeny with both Ty1 and Ty3 (Ty1/Ty3 genotype). Then, now you will have both Ty1 and Ty2 alleles in a specific elite cultivar.
There might be other methods to develop it.
2. Regarding which allele confer higher resistance, you need to do experiment to decide it. If there is an 'additive effect' presence, the elite cultivar with both Ty1 and Ty3 alleles should confer higher resistance than those elite cultivar with only Ty1 or Ty3 allele alone
1. I don't know. Do you have a resistant line with both Ty-1 and Ty-3 alleles (Genotype: Ty-1/Ty-3)? Or, do you at least have resistant lines with only Ty-1 OR Ty-3 allele (Genotype Ty-1/- or Ty-3/-) for your research?
2. If you have resistant lines with only Ty-1 or Ty-3 allele. you can still make backcross separately. Then, above scheme can be modified as following:
(1) Backcross resistant line (Ty1/-) several runs with the elite line (-/-) to regain elite line genetic background (select the exist of Ty1 allele after each backcross). Let's say the find product is Elite line Ty1.
(2) At the same time, backcross resistant line (Ty3/-) several runs with the same elite line (-/-) to regain elite line genetic background (select the exist of Ty3 allele after each backcross). Let's say the find product is Elite line Ty3.
(3) Make a cross between (Elite line Ty1) and (Elite line Ty3); select progeny with both Ty1 and Ty3 (Ty1/Ty3 genotype). Then, now you will have both Ty1 and Ty2 alleles in a specific elite cultivar.
3. Do you have these kinds of resistant lines (ie. Ty1/- and Ty-3) for your experiments? Are they 'wild' (not domesticated)? If they are wild, do these wild line and elite cultivar crossable in this plant species?
4. How do you distinguish Ty-1 and Ty-3 alleles, in terms of the difference of their DNA sequences? Have Ty-1 and Ty-3 been cloned and their sequences known? Are their sequences highly conserved if their sequences are known? Can they be distinguished by a simple PCR amplification?
This is good. You have most info ready to proceed your research. Can the 'wild (not domesticated)' plant and the elite cultivar crossable (readily pollinate to each other) and produce fertile progeny?
It is very hard to complete it in a short period of time because you need to do backcross several generations to achieve your goal. This may take several years, even if you apply marker-assistant backcrossing approach.
Can you just clone these two genes and genetically transform them into the elite line?