Net income €6,250
Home loan: €1,750
Child care and other: €1,200
Available for other expenses : €3,300
so you have plenty left over
Rent received: €900
Interest cost: €1,050
Loss: €150 per month. - €1,800 per year + the other costs of ownership
OK, so this is not a great investment, but it's not that bad either. It's not losing you too much, although it will be a drain on your cash.
You won't get any deal from the lender as you have cash and a very good income.
Your figures are a bit confusing
Mortgage E238,000 ... I can reduce this debt down to E168000 with savings.
€238k down to €168k is €70k, but you say "
Other savings and investments E110000"
I assume you do have €110,000 which means you can eliminate the negative equity on either loan.
So, what should you do with your €110,000?
Option 1 - Reduce the mortgage on the Buy to Let to €118,000 and then you can sell it. You won't have an investment property and you won't have an investment mortgage.
This is probably the best option. It's losing money. Losses will probably increase as interest rates rise. If property prices rise, you will benefit anyway as you have a house worth €230,000.
Option 2 - Reduce the mortgage on the Buy to let but keep it
You will save
€110,000 @5.4% =€ 5,940
Tax relief = €2,222 (€5,940 @ 75% @50%)
Net saving: €3,721
Option 3 Reduce the mortgage on your home
€110,000 @ 4.4% = €4,400
It makes better financial sense to pay down the mortgage on your home, if you are going to keep the investment property.