Why on earth would you buy a second house and keep the first one sitting empty? You'd have all the hassle of having a second property in terms of 2 x maintenance bills etc (an empty house can need more maintenance if it isn't kept heated and ventilated), 2 x council tax plus having to pay extra capital gains tax if you ever came to sell the house that isn't your main residence. And you'd be getting no active return on the capital tied up in the property so your only return on investment would be in increase in property prices which isn't necessarily that great depending on where in the country you are. Plus it is a very non-liquid asset (meaning if you urgently needed the cash e.g. in case of your DH being made redundant) it would take a long time to get it as you would have to wait for the house to sell. So overall I think your DH's plan is not a good one 
Buy to let is not as good an investment as it was (property price growth in a lot of areas of the country has stalled, plus you are taxed much more on the income than used to be the case), and as you rightly say can require quite a lot of input in managing the property and dealing with tenants (you can get managing agents to do a lot for you but that further eats in to your profits). Also for most people the bulk of their capital/savings is already invested in property in the form of their main residence so whilst property/real estate is usually overall a safe investment, investing in more property means all their eggs are in one basket, if the market crashes they cannot then move money around until it recovers which can take years. So I wouldn't advise that either.
As to what I would do in your position, it slightly depends. What is the motivation for wanting a bigger property, are you overcrowded in your current house/significant problems in current home? You say you could afford a 'posh' area if you moved, what would this actually mean for your family in tangible terms - better education, safer/lower crime, shorter commute, closer to family? Usually if it's purely a space/'kerb appeal' you are better off spending money on an extension to add space to your current home or remodelling and redecorating e.g. to create open plan space, if this is possible. You don't always see the full amount spent added to the value of the home so it's not an investment as such but it's much better value than having to spend lots of money on estate agents, solicitors, stamp duty etc. on moving home, which really is money down the drain. But if moving home would mean better schools or a much better quality of life that you couldn't get in your current home, of course that is different. Most people do have mortgages so whilst your fears about locking yourself in and overstretching are rational and natural I think taking out a relatively small mortgage wouldn't be a terrible idea if your family will benefit overall.
Also your fears about your husbands job, what is that based on? Is there a real likelihood of redundancy and if so what's his package like? Realistically how long will it take him to find another job - weeks, months or years? This will guide how much money you want to keep in 'cash' (not actual cash of course but in a form you can easily access such as a cash ISA or instant access savings account).
In a nutshell, assuming there's no massively significant need to move home and your husband has a reasonable redundancy entitlement and could find replacement employment within 6 months or so, I would probably:
-Keep 6 months expenses less the redundancy package in an easy access savings account
-Stick in current home, perhaps set aside a small amount from savings for home improvements.
-Max out pensions entitlements and ISA allowances for you both for this year, if you haven't already done so, and keep enough cash to use up next year's entitlements too. Get a SIPP if your work pension schemes aren't great.
-Put the rest into a low or medium risk investment fund - do your research into these but there are funds/websites which perform well and require minimal input from you, you simply set your risk level. I use nutmeg.
Hope this helps!