With income of €100k, you are not going to get a mortgage of €280k when you already have mortgages totalling €370k.
I presume that the rental property was bought as an investment and not as her home before you got married? In case it was her home before you got married, there is a possibility, that the lender would allow her to move it to the proposed property.
You seem to be getting on very well and have sorted almost everything out amicably so far. While everything is amicable, you should make every effort to separate yourselves financially from each other. Even if that is not the most efficient financially. For example, it is usually a good idea to hold onto an investment property with a tracker, but in this case, you will probably have to sell it. It's just one more connection with your ex, that could be a source of conflict. (Or put it into her sole name.)
After that is sold, she will have €190k and so would need a mortgage of €130k.
That is just about doable.
If your two existing mortgages are with the one lender, it might be easier to do.
Here are the potential outcomes
1) Talk to the lender on the investment property and ask them can you transfer the mortgage to a new property in her name only. They will probably refuse but ask anyway. It might suit them as they will up the mortgage rate by about 1%. The ten years remaining will be a problem as she won't be able to repay it over that term. She will need an extension.
2) If that does not work, ask other lenders if they will give her a mortgage of €130k. They probably will.
If so, sell the rental and she buys her house.
3) If she cannot get a mortgage, then put the rental property in her sole name. Try to get the mortgage into her sole name. If they won't agree, you just have to live with the risk.
You own your home. She owns hers.
She rents a suitable house until she has paid down more of the rental mortgage and has enough equity to buy a house.
You will need to do some adjustment. Even if the rent she receives is the same as the rent she is paying, she will be paying tax on the rent received. You could pay something like half the tax on the rental income to balance things out.
4) Last resort option. Sell the investment property and buy a family home for her in both your names. You should try the other options first. But if this is the only way of getting her a family home, then you have to live with it.
Brendan