Should I buy second btl

Have a btl with £136k mortgage, up for renewal end of year. Mortgage will increase from £250 to around £556, my broker has said.
Have had a windfall of £150k, so could pay off. We get £10k a year rental income before tax. Have worked out I would get around £2,200 a year after tax if I continue with new higher mortgage. It is in my name.
However, husband and I are thinking of buying his sister out of his late father’s flat, which has been on market for three months now. We would use my £150k and around £35k from savings to do this, plus his half. Flat would rent for around £14k a year.
There would be no mortgage on the new property but it would take most of our savings. I work full time, in lower tax bracket. Combined rental income would take me into higher bracket, but could offset this as husband a pensioner and I could drop a day at work.
We have two kids who will struggle to get on property ladder. Idea would be to rent to tenants for next few years, we would be in it for long term.
We are in a real dilemma and would welcome advice

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As a parent and landlord I could buy more properties but My kids come fiirst. I was doing up a place to rent out and thinking about my daughter who was renting , I thought I do not need the money, they will notget on the property ladder so I gave it to them . I am just about to buy a place fo my son who is a gardener. You get my drift. I only live now to help them before I die . Kids first with me . But I will be older than you ! Maybe depends on how old the kids are and if you can help them later on and still live comfotably. Also I have no motgages. We all view life differently

I wouldnt recommend it. Apart from fact property prices are widely expected to fall the most important aspect of having investments is diversification and buying it would mean you would have everything in property which isn’t accessible if you need it and you would be significantly impacted if you had a bad tenant.

You will also pay a lot of tax. If you were to invest it ISA portfolio of funds your returns would be tax free and would provide a fund that could provide you with an income and/or help children which would be more suitable for most people.

Yes, think it would be more clear cut if we had no mortgage on one!

Sorry, meant to reply to Colin.

Thank you for your response. Yes, the putting all the eggs into one basket aspect is the one biggest obstacle. We have a long term couple - 14 years - in the mortgaged property, but the second one, if we bought, would be an unknown quantity. We use a good management company but it’s a risk.
Thank you for your advice. We are seeing our accountant on Weds and if he advises against it, I will pay off the first mortgage and look into ISAs etc

Maybe pay a sum off the Mortgage and still help the children? Having extra cash is always tempting to spend on another property. Each of us will make a different decision ,depending on our age , childrens age, our heath, how much we earn job security and so on